Distance Between Two Lines

Let the slope be m of the straight line which passes through

(-2%2C2)%2C

then equation

(y-2)%3Dm(x%2B2)

mx-y%2B(2m%2B2)%3D0

..(i)

%5Cbecause

Perpendicular distance of line (i) from point (given)

(3%2C-1)%3D6

%5CRightarrow

%5Cfrac%7B%7Cm(3)-(-1)%2B(12m%2B2)%7C%7D%7B%5Csqrt%7B%7B%7Bm%7D%5E%7B2%7D%7D%2B%7B%7B(-1)%7D%5E%7B2%7D%7D%7D%7D%3D6

%7C3m%2B1%2B2m%2B2%7C%3D6%5Csqrt%7B%7B%7Bm%7D%5E%7B2%7D%7D%2B1%7D

Squaring on both sides,

%5CRightarrow

%7B%7B(5m%2B3)%7D%5E%7B2%7D%7D%3D36(%7B%7Bm%7D%5E%7B2%7D%7D%2B1)

%5CRightarrow

25%7B%7Bm%7D%5E%7B2%7D%7D%2B9%2B30m%3D36%7B%7Bm%7D%5E%7B2%7D%7D%2B36

%5CRightarrow

11%7B%7Bm%7D%5E%7B2%7D%7D-30m%2B27%3D0

..(ii)
Now,

%5CDelta%20%3D%7B%7BB%7D%5E%7B2%7D%7D-4AC%3D900-4(11)%5C%2C(27)%20%3C%200

%5Cbecause

Discriminate of E (ii) is negative. i.e., slope of the given line is imaginary. So, no line drawn through the point

(2%2C2)

Chapter Questions
1 MCQs