Question

In the parabola y² = 4x, the tangent at the point P, whose abscissa is equal to the latus rectum, meets the axis at T and the normal at P cuts the curve again at Q. Then the ratio PT : PQ is

 (A)   5 : 4

(B)   4 : 5

(C)   2 : 3

(D)   3 : 2

Answer 1

Correct option (B) 4 : 5

Explanation :

 We have

y² = 4ax(a = 1)

 By hypothesis, at P = (4, 4) so that the tangent equation at P (4, 4) is 2y = x + 4 which implies that

T = (-4,0)   ....(1)

 Also the normal at P(4, 4) meets the curve again at Q (t² 2t). So

t = -2 - 2/2 = -3

so that Q = 9, - 6). Now