Question

Tangents are drawn from the points on the line x – y + 3 = 0 to parabola y2 = 8x. Then the variable chords of contact pass through a fixed point whose coordinates are

(A) (3, 2)

(B) (2, 4)

(C) (3, 4)

(D) (4, 1)

Answer 1

Correct Answer is: (C) (3, 4)

Let point P(x1 , y1 )

x1 – y1 + 3 = 0

C.O.C.w.r.t. (x1 , y1 ) of y2 = 4ax

yy1 = 4(x + x1 )

y(x1 + 3) = 4x + 4x1

yx1 + 3y – 4x – 4x1 = 0

(3y – 4x) + x1 (y – 4) = 0

L1 + λL2 = 0

L1 = 0 & L2 = 0

3y = 4x y = 4

x = 3

point (3, 4)