Parabola

A beam is supported at its ends by supporters which are 12 meters apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm?

The volume of the cylindrical column standing on the area common to the parabolas , and cut off by the surface is:

If a Chord which is normal to the parabola y² = 4ax at one end subtends a right angle at the vertex, then its slope is -

Match List-I and List-II

LIST I		LIST II
A.	The angle between the straight lines, 2x2+ 3y2-7xy=0 is	I.
B.	The circles x2+y2+x+y=0 and x2+y2 +x-y=0 intersect at angle	II.	25π
C.	The area of circle centered at (1,2) and passing through (4,6) is	III.	π/4
D.	The parabola y2=4x and x2 =32y intersect at point (16,8) at angle	IV.	π/2

Choose the correct answer from the options given below:

The area bounded by two parabolas y= x², x=y² is,

The equation of the parabola which is symmetric about the y-axis and has its vertex at origin and passes through the point (1, -1) is