JEE-MAIN SERIES Mathematics
Conic Sections
120 previous year questions.
Volume: 120 Ques
Yield: High
High-Yield Trend
25
2026 6
2025 8
2024 8
2023 13
2022 22
2021 3
2020 12
2019 2
2018 4
2016 5
2015 5
2014 7
2013 Chapter Questions 120 MCQs
01
PYQ 2013
hard
mathematics ID: jee-main
A common tangent to the conics and is:
1
2
3
4
02
PYQ 2013
medium
mathematics ID: jee-main
A tangent to the hyperbola meets x-axis at and y-axis at . Lines and are drawn such that is a rectangle (where is the origin). Then lies on :
1
2
3
4
03
PYQ 2013
medium
mathematics ID: jee-main
The equation of the circle passing through the foci of the ellipse and having centre at (0, 3) is
1
2
3
4
04
PYQ 2013
medium
mathematics ID: jee-main
The ellipse = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse is
1
2
3
4
05
PYQ 2013
medium
mathematics ID: jee-main
If two vertices of an equilateral triangle are and , and the third vertex lies above x-axis then the equation of the circumcircle of is :
1
2
3
4
06
PYQ 2013
medium
mathematics ID: jee-main
Let the equations of two ellipses be , If the product of their eccentricities is , then the length of the minor axis of ellipse is:
1
2
3
4
07
PYQ 2013
easy
mathematics ID: jee-main
Statement 1 : The only circle having radius and a diameter along line Statement 2 : is a normal to the circle
1
Statement 1 is false; Statement 2 is true
2
Statement 1 is true; Statement 2 is true, Statement 2 is a correct explanation for Statement 1
3
Statement 1 is true; Statement 2 is false
4
Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1
08
PYQ 2014
medium
mathematics ID: jee-main
Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y) passing through origin and touching the circle externally, then the radius of is equal to
1
2
3
4
09
PYQ 2014
medium
mathematics ID: jee-main
Let be the length of the common chord of the curves and and be the length of the latus rectum of then :
1
2
3
4
10
PYQ 2014
medium
mathematics ID: jee-main
Let P and Q where be two distinct points on the hyperbola Then the ordinate of the point of intersection of the normals at P and Q is :
1
2
3
4
11
PYQ 2014
medium
mathematics ID: jee-main
Two tangents are drawn from a point to the curve, If is the angle between them, then is equal to :
1
2
3
4
12
PYQ 2014
medium
mathematics ID: jee-main
The slope of the line touching both the parabolas and is :
1
2
3
4
13
PYQ 2015
easy
mathematics ID: jee-main
An ellipse passes through the foci of the hyperbola, an and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is then which of the following points does not lie on the ellipse ?
1
2
3
4
14
PYQ 2015
medium
mathematics ID: jee-main
If is the equation of a chord of the circle, , then the equation of the circle with this chord as diameter is :
1
2
3
4
15
PYQ 2015
medium
mathematics ID: jee-main
Let be the vertex and be any point on the parabola, = 8y. If the point divides the line segment internally in the ratio , then the locus of is
1
2
3
4
16
PYQ 2015
medium
mathematics ID: jee-main
Let be a double ordinate of the parabola, , where P lies in the second quadrant. If R divides in the ratio , then the locus of R is :
1
2
3
4
17
PYQ 2015
medium
mathematics ID: jee-main
Locus of the image of the point in the line is a
1
Straight line parallel to x-axis
2
Straight line parallel to y-axis
3
Circle of radius
4
Circle of radius
18
PYQ 2016
easy
mathematics ID: jee-main
If the tangent at a point on the ellipse meets the coordinate axes at A and B, and O is the origin, them the minimum area (in s units) of the triangle OAB is:
1
2
3
4
19
PYQ 2016
medium
mathematics ID: jee-main
A hyperbola whose transverse axis is along the major axis of the conic, and has vertices at the foci of this conic. If the eccentricity of the hyperbola is , then which of the following points does NOT lie on it ?
1
(0, 2)
2
, 2
3
, 2
4
20
PYQ 2016
medium
mathematics ID: jee-main
Equation of the tangent to the circle, at the point , whose centre is the point of intersection of the straight lines and is :
1
2
3
4
21
PYQ 2016
medium
mathematics ID: jee-main
and are two distinct points on the parabola, , with parameters and respectively. If the normal at passes through , then the minimum value of is :
1
2
2
4
3
6
4
8
22
PYQ 2018
medium
mathematics ID: jee-main
If the length of the latus rectum of an ellipse is units and the distance between a focus and its nearest vertex on the major axis is units, then its eccentricity is :
1
2
3
4
23
PYQ 2018
medium
mathematics ID: jee-main
If the tangent at to the curve touches the circle then the value of c is:
1
195
2
185
3
85
4
95
24
PYQ 2019
medium
mathematics ID: jee-main
A hyperbola has its centre at the origin, passes through the point and has transverse axis of length along the x-axis. Then the eccentricity of the hyperbola is :
1
2
3
4
25
PYQ 2019
medium
mathematics ID: jee-main
If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is , then the length (in cm) of their common chord is :
1
2
3
4
26
PYQ 2019
medium
mathematics ID: jee-main
If one end of a focal chord of the parabola, is at then the length of this focal chord is
1
25
2
24
3
20
4
22
27
PYQ 2019
medium
mathematics ID: jee-main
If a circle passing through the point touches the circle externally at the point , then the radius of is :
1
2
3
4
28
PYQ 2019
medium
mathematics ID: jee-main
If a circle of radius passes through the origin and intersects the coordinate axes at and , then the locus of the foot of perpendicular from on is :
1
2
3
4
29
PYQ 2019
medium
mathematics ID: jee-main
Axis of a parabola lies along -axis. If its vertex and focus are at distances and respectively from the origin, on the positive -axis then which of the following points does not lie on it ?
1
2
3
4
30
PYQ 2019
medium
mathematics ID: jee-main
Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If 'S'BS is a right angled triangle with right angle at B and area ( S'BS) = 8 s units, then the length of a latus rectum of the ellipse is :
1
2
2
3
4
4
4
31
PYQ 2019
medium
mathematics ID: jee-main
A circle touching the x-axis at and making an intercept of length on the y-axis passes through the point :
1
(3, 10)
2
(2,3)
3
(1,5)
4
(3,5)
32
PYQ 2019
medium
mathematics ID: jee-main
A circle cuts a chord of length on the x-axis and passes through a point on the y-axis, distant from the origin. Then the locus of the centre of this circle, is :
1
A hyperbola
2
A parabola
3
A straight line
4
An ellipse
33
PYQ 2019
medium
mathematics ID: jee-main
Let and be points on the
parabola, . Let be chosen on the arc of the parabola, where is the origin, such that the area of is maximum. Then, the
area (in s units) of , is :
1
2
32
3
4
34
PYQ 2019
medium
mathematics ID: jee-main
An ellipse, with foci at (0, 2) and (0, -2) and minor axis of length 4, passes through which of the following points?
1
(1,2√2)
2
(2,√2)
3
(2,2√2)
4
(√2,2)
35
PYQ 2019
medium
mathematics ID: jee-main
Two circles with equal radii are intersecting at the points and . The tangent at the point to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :
1
2
3
4
36
PYQ 2020
medium
mathematics ID: jee-main
The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, , internally in the ratio 1 : 2, is :
1
2
3
4
37
PYQ 2020
hard
mathematics ID: jee-main
If a hyperbola passes through the point and it has vertices at , then the equation of the normal to it at P is :
1
2
3
4
38
PYQ 2020
medium
mathematics ID: jee-main
Let the latus ractum of the parabola be the common chord to the circles and each of them having radius . Then, the distance between the centres of the circles and is:
1
2
3
4
39
PYQ 2021
medium
mathematics ID: jee-main
If the curve intersects the line at two points P and Q, then the angle subtended by the line segment PQ at the origin is :
1
2
3
4
40
PYQ 2021
medium
mathematics ID: jee-main
A hyperbola passes through the foci of the ellipse and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:
1
2
3
4
41
PYQ 2021
medium
mathematics ID: jee-main
A tangent is drawn to the parabola y² = 6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it ?
1
(0, 3)
2
(-6, 0)
3
(5, 4)
4
(4, 5)
42
PYQ 2021
medium
mathematics ID: jee-main
Consider a hyperbola H: x² - 2y² = 4. Let the tangent at a point P(4, √6) meet the x-axis at Q and latus rectum at R(x₁, y₁), x₁>0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR is equal to :
1
√6 - 1
2
7/√6 - 2
3
4√6 - 1
4
4√6
43
PYQ 2021
medium
mathematics ID: jee-main
A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity and the distance of the nearer focus from this directrix is , then the equation of the other directrix can be :
1
or
2
or
3
or
4
or
44
PYQ 2021
medium
mathematics ID: jee-main
Let an ellipse , passes through and has eccentricity . If a circle, centered at focus , of and radius , intersects at two points and , then is equal to :
1
2
3
4
45
PYQ 2021
medium
mathematics ID: jee-main
Let A(sec , 2tan ) and B(sec , 2tan ), where , be two points on the hyperbola . If ( , ) is the point of the intersection of the normals to the hyperbola at A and B, then is equal to _________.
46
PYQ 2021
medium
mathematics ID: jee-main
A circle C touches the line at the point (2, 1) and intersects the circle C : at two points P and Q such that PQ is a diameter of C . Then the diameter of C is :
1
15
2
3
4
47
PYQ 2021
medium
mathematics ID: jee-main
Let a tangent be drawn to the ellipse x²/27 + y² = 1 at (3 cosθ, sinθ) where θ ∈ (0, π/2). Then the value of θ such that the sum of intercepts on axes made by this tangent is minimum is equal to :
1
π/3
2
π/6
3
π/8
4
π/4
48
PYQ 2021
medium
mathematics ID: jee-main
The point P lies on the hyperbola having eccentricity . If the tangent and normal at P to the hyperbola intersect its conjugate axis at the points Q and R respectively, then QR is equal to :
1
2
3
6
4
49
PYQ 2021
medium
mathematics ID: jee-main
The locus of the mid points of the chords of the hyperbola , which touch the parabola , is :
1
2
3
4
50
PYQ 2021
medium
mathematics ID: jee-main
If a line along a chord of the circle , passes through the point and is tangent to the parabola , then the length of this chord is :
1
7
2
3
5
4
51
PYQ 2021
medium
mathematics ID: jee-main
On the ellipse let be a point in the second quadrant such that the tangent at to the ellipse is perpendicular to the line . Let and be the foci of the ellipse and be its eccentricity. If is the area of the triangle then, the value of is :
1
24
2
14
3
12
4
6
52
PYQ 2021
medium
mathematics ID: jee-main
If two tangents drawn from a point P to the parabola are at right angles, then the locus of point P is :
1
x + 1 = 0
2
x + 2 = 0
3
x + 3 = 0
4
x + 4 = 0
53
PYQ 2021
medium
mathematics ID: jee-main
A tangent line L is drawn at the point on the parabola . If the line L is also tangent to the circle , then 'a' is equal to _________.
54
PYQ 2021
medium
mathematics ID: jee-main
Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, -4), one focus at (4, -4) and one vertex at (5, -4). If is a tangent to the ellipse E, then the value of is equal to ________.
55
PYQ 2021
medium
mathematics ID: jee-main
Let a parabola be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from to the parabola which meet at and , then the area (in sq. units) of is equal to :
1
2
3
4
56
PYQ 2021
medium
mathematics ID: jee-main
The locus of the centroid of the triangle formed by any point P on the hyperbola , and its foci is :
1
2
3
4
57
PYQ 2021
medium
mathematics ID: jee-main
For which of the following curves, the line x + √3 y = 2√3 is the tangent at the point (3√3 / 2, 1/2) ?
1
x² + y² = 7
2
y² = (1 / 6√3) x
3
2x² - 18y² = 9
4
x² + 9y² = 9
58
PYQ 2021
medium
mathematics ID: jee-main
A line is a common tangent to the circle and the parabola . If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a+c) is equal to ________ .
59
PYQ 2021
medium
mathematics ID: jee-main
The locus of the point of intersection of the lines (√3)kx + ky - 4√3 = 0 and √3 x - y - 4(√3)k = 0 is a conic, whose eccentricity is _________
60
PYQ 2021
medium
mathematics ID: jee-main
If the curves, x²/a + y²/b = 1 and x²/c + y²/d = 1 intersect each other at an angle of 90°, then which of the following relations is TRUE?
1
a + b = c + d
2
a - b = c - d
3
ab / (a+b) = (c+d)/(a+b)
4
a - c = b + d
61
PYQ 2022
hard
mathematics ID: jee-main
For the hyperbola and the ellipse , let the
(1) eccentricity of E be reciprocal of the eccentricity of H, and
(2) the line be a common tangent of E and H.
Then is equal to _______.
(1) eccentricity of E be reciprocal of the eccentricity of H, and
(2) the line be a common tangent of E and H.
Then is equal to _______.
62
PYQ 2022
hard
mathematics ID: jee-main
A line, with the slope greater than one, passes through the point A (4,3) and intersects the line x-y-2=0 at the point B If the length of the line segment AB is then B also lies on the line :
1
2 x+y=9
2
3 x-2 y=7
3
x+2 y=6
4
2 x -3 y =3
63
PYQ 2022
hard
mathematics ID: jee-main
Let be the plane containing the straight line and perpendicular to the plane containing the straight lines and If is the distance of from the point , then is equal to :
1
2
96
3
4
54
64
PYQ 2022
medium
mathematics ID: jee-main
If and , are two common tangents of circle and parabola , then the value of is equal to :
1
2
3
4
65
PYQ 2022
medium
mathematics ID: jee-main
Let be the mirror image of the point with respect to the plane : . If a line L passing through , parallel to the line meets the plane at , then is equal to :
1
2
2
5
3
7
4
11
66
PYQ 2022
medium
mathematics ID: jee-main
Let be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then is equal to
1
2
3
4
67
PYQ 2022
medium
mathematics ID: jee-main
Let the lines
and
be normal to a circle . If the line
is tangent to the circle C, then the value of is equal to _______.
and
be normal to a circle . If the line
is tangent to the circle C, then the value of is equal to _______.
68
PYQ 2022
easy
mathematics ID: jee-main
Let the tangent drawn to the parabola y2 = 24x at the point (α, β) is perpendicular to the line 2x + 2y = 5. Then the normal to the hyperbola
at the point (α + 4, β + 4) does NOT pass through the point
1
(25, 10)
2
(20, 12)
3
(30, 8)
4
(15, 13)
69
PYQ 2022
easy
mathematics ID: jee-main
Let the common tangents to the curves 4(x2 + y2) = 9 and y2 = 4x intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and I respectively denote the eccentricity and the length of the latus rectum of this ellipse, then
is equal to
70
PYQ 2022
hard
mathematics ID: jee-main
An ellipse
passes through the vertices of the hyperbola
Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be 1/2. If the length of the latus rectum of the ellipse E, then the value of 113l is equal to _____.
71
PYQ 2022
hard
mathematics ID: jee-main
A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of is equal to ________ .
72
PYQ 2022
hard
mathematics ID: jee-main
A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola where . Then is equal to ___________.
73
PYQ 2022
medium
mathematics ID: jee-main
Let l be a line which is normal to the curve at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to _________ .
74
PYQ 2023
hard
mathematics ID: jee-main
The equations of two sides of a variable triangle are and , and its third side is a tangent to the parabola . The locus of its circumcentre is:
1
2
3
4
75
PYQ 2023
medium
mathematics ID: jee-main
Let the foci of the ellipse and the hyperbola coincide Then the length of the latus rectum of the hyperbola is:-
1
2
3
4
76
PYQ 2023
hard
mathematics ID: jee-main
A parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola
1
y2 = 16x
2
y2 = 4x
3
y2 = 8x
4
x2 = 4y
77
PYQ 2023
medium
mathematics ID: jee-main
If the tangent at a point 𝑃 on the parabola is parallel to the line and the tangents at the points 𝑄 and 𝑅 on the ellipse are perpendicular to the line 𝑥−𝑦=2, then the area of the triangle PQR is :
1
2
3
4
78
PYQ 2023
medium
mathematics ID: jee-main
Consider ellipse , for . Let be the circle which touches the four chords joining the end points (one on the minor axis and another on the major axis) of the ellipse . If is the radius of the circle , then the value of is:
1
3320
2
3210
3
3080
4
2870
79
PYQ 2023
medium
mathematics ID: jee-main
Let the tangent to the parabola at the point (3, α) be perpendicular to the line 2x + 2y = 3. Then the square of distance of the point (6, – 4) from the normal to the hyperbola at its point (α– 1, α + 2) is equal to__
80
PYQ 2023
hard
mathematics ID: jee-main
The set of all values of for which the line bisects two distinct chords drawn from a point on the circle , is equal to :
1
2
3
4
81
PYQ 2023
medium
mathematics ID: jee-main
Let . Let be the smallest even value of such that the eccentricity of is a rational number. If is the length of the latus rectum of , then 21 is equal to:
82
PYQ 2024
medium
mathematics ID: jee-main
Let be the eccentricity of the hyperbola $ be the eccentricity of the ellipse \) $ which passes through the foci of the hyperbola. If , then the length of the chord of the ellipse parallel to the x-axis and passing through (0, 2) is:
1
2
3
4
83
PYQ 2024
hard
mathematics ID: jee-main
The area (in square units) of the region enclosed by the ellipse $ $ in the first quadrant below the line is:
1
2
3
4
84
PYQ 2024
medium
mathematics ID: jee-main
The sum of squares of all possible values of , for which the area of the region bounded by the parabolas is maximum, is equal to:
85
PYQ 2024
medium
mathematics ID: jee-main
Let be the focus of the hyperbola , on the positive x-axis. Let be the circle with its centre at and passing through the point . If is the origin and is a diameter of , then the square of the area of the triangle is equal to -
86
PYQ 2024
hard
mathematics ID: jee-main
Let the latus rectum of the hyperbola subtend an angle of at the center of the hyperbola. If is equal to , where and are coprime numbers, then is equal to .
87
PYQ 2024
easy
mathematics ID: jee-main
Let and be three points on the parabola , and let the line segment meet the line through parallel to the -axis at the point . Let and respectively be the feet of the perpendiculars from and on . Then is equal to ______ .
88
PYQ 2024
medium
mathematics ID: jee-main
For , if the eccentricity of the hyperbola is times the eccentricity of the ellipse , then the value of is:
1
2
3
4
89
PYQ 2024
easy
mathematics ID: jee-main
Let the foci of a hyperbola coincide with the foci of the ellipse and the eccentricity of the hyperbola be the reciprocal of the eccentricity of the ellipse . If the length of the transverse axis of is and the length of its conjugate axis is , then is equal to:
1
242
2
225
3
237
4
205
90
PYQ 2025
medium
mathematics ID: jee-main
Let
Let the distance between the foci of and the foci of be . If , and the ratio of the eccentricities of and is , then the sum of the lengths of their latus rectums is equal to:
1
9
2
10
3
8
4
7
91
PYQ 2025
medium
mathematics ID: jee-main
If and are the foci of the ellipse and is a point on the ellipse, then is equal to:
1
2
3
9
4
27
92
PYQ 2025
medium
mathematics ID: jee-main
Let the ellipse pass through the centre of the circle of radius . Let be the focal distances of the point on the ellipse. Then is equal to
1
2
3
4
93
PYQ 2025
medium
mathematics ID: jee-main
Consider the hyperbola
having one of its foci at . If the latus rectum through its other focus subtends a right angle at , and
then find and .
94
PYQ 2025
easy
mathematics ID: jee-main
Let one focus of the hyperbola be at and the corresponding directrix be . If and respectively are the eccentricity and the length of the latus rectum of , then is equal to:
1
14
2
16
3
18
4
12
95
PYQ 2025
medium
mathematics ID: jee-main
Let $ E H 2\sqrt{3} a - A = 2 E H \frac{1}{3}$, then the sum of the lengths of their latus rectums is equal to:
1
8
2
10
3
9
4
7
96
PYQ 2026
medium
mathematics ID: jee-main
Consider the parabola and the ellipse . Let the line segment joining the points of intersection of and , be their latus rectum. If the eccentricity of is , then is equal to ____.
97
PYQ 2026
medium
mathematics ID: jee-main
Let O be the origin, and P and Q be two points on the rectangular hyperbola such that the midpoint of the line segment PQ is . Then the area of the triangle OPQ equals:
1
2
3
4
98
PYQ 2026
medium
mathematics ID: jee-main
Let be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is . If the line intersects the hyperbola H at the points A and B such that the area of the triangle AOB is , where O is the origin, then equals:
1
12
2
16
3
24
4
25
99
PYQ 2026
easy
mathematics ID: jee-main
Let and be the foci of the ellipse
and be a point on the ellipse in the first quadrant. If
then is equal to
1
17
2
13
3
15
4
11
100
PYQ 2026
medium
mathematics ID: jee-main
If ellipse
and hyperbola
have the same foci. If eccentricity and length of latus rectum of the hyperbola are and respectively, then find the value of .
1
2
3
4
101
PYQ 2026
medium
mathematics ID: jee-main
Let one end of a focal chord of the parabola be . If divides this focal chord internally in the ratio , then the minimum value of is equal to :
1
5
2
7
3
16
4
22
102
PYQ 2026
easy
mathematics ID: jee-main
Points of intersection of ellipses and lie on a circle. Value of is
1
53
2
51
3
55
4
52
103
PYQ 2026
easy
mathematics ID: jee-main
If the line , where , touches the ellipse at the point in the first quadrant, then one of the focal distances of is :
1
2
3
4
104
PYQ 2026
medium
mathematics ID: jee-main
Let mirror image of parabola in the line be . Then the value of is
1
3
2
6
3
9
4
12
105
PYQ 2026
hard
mathematics ID: jee-main
Let be the focus of the parabola .
Let the line intersect the parabola at two distinct points and .
If the centroid of triangle is ,
then is equal to:
1
2
3
4
106
PYQ 2026
easy
mathematics ID: jee-main
Let the ellipse
and the hyperbola
have the same foci. If and respectively denote the eccentricity and the length of the latus rectum of ,
then the value of is:
1
2
3
4
107
PYQ 2026
medium
mathematics ID: jee-main
Let f be a twice differentiable non-negative function such that . Then the mean of is equal to :
108
PYQ 2026
hard
mathematics ID: jee-main
Let and be two parabolas. If the area of the bounded region enclosed between and is six times the area of the bounded region enclosed between the line , the line , and , then the required value is:
1
2
3
4
109
PYQ 2026
hard
mathematics ID: jee-main
For some , let the eccentricity and the length of the latus rectum
of the hyperbola
be and , respectively, and let the eccentricity and the length of the latus rectum of the ellipse
be and , respectively.
If
then
is equal to:
110
PYQ 2026
medium
mathematics ID: jee-main
Let be a point on the hyperbola
whose foci are and . If the length of its latus rectum is , then the square of the area of is equal to
1
4200
2
900
3
1462
4
2700
111
PYQ 2026
easy
mathematics ID: jee-main
Let be the parabola with its vertex at . Let be a point on the parabola and be a point on the -axis such that . Then the locus of the centroid of such triangles is :
1
2
3
4
112
PYQ 2026
medium
mathematics ID: jee-main
Let O be the vertex of the parabola and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2:3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is:
1
2
3
4
113
PYQ 2026
easy
mathematics ID: jee-main
Let mirror image of parabola in the line be . Then the value of is
114
PYQ 2026
easy
mathematics ID: jee-main
Let and be vectors such that
and
If ( ) are the possible values of
then the equation
represents a circle, for equal to
1
2
2
-1
3
1
4
4
115
PYQ 2026
medium
mathematics ID: jee-main
Let the foci of a hyperbola coincide with the foci of the ellipse . If the eccentricity of the hyperbola is 5, then the length of its latus rectum is:
1
2
12
3
16
4
116
PYQ 2026
medium
mathematics ID: jee-main
Let , from point a focal chord is passing. Point divides the focal chord in the ratio 2:3, then the minimum value of is:
117
PYQ 2026
medium
mathematics ID: jee-main
The value of for which the line never touches the hyperbola
is:
1
2
3
4
118
PYQ 2026
medium
mathematics ID: jee-main
Ellipse , A hyperbola confocal with ellipse and eccentricity of hyperbola is equal to 5. The length of latus rectum of hyperbola is, if principle axis of hyperbola is x-axis?
1
2
3
4
119
PYQ 2026
medium
mathematics ID: jee-main
Consider an ellipse
where for both the curves and is the length of latus rectum of and is the length of latus rectum of . Let the distance between the foci of the first curve be . Find the distance between the foci of the second curve. (Given ).
1
2
3
4
120
PYQ 2026
medium
mathematics ID: jee-main
An ellipse has its centre at , one focus at and one vertex at .
Then the length of its latus rectum is:
1
2
3
4