Question

From the point (15, 12) three normals ae drawn to the parabola y2 = 4x, then centroid of triangle formed by three co-normal points is

(a) (5, 0)

(b) (5, 4)

(c) (9, 0)

(d) (26/3 , 0)

Answer 1

Correct option (d) (26/3, 0)

Explanation:

Let equation of normal be y = –tx + 2t + t3

It passes through (15, 12).

So 12 = –15t + 2t + t3

t3 –13t –12 = 0

(t + 1) ( t + 3) (t – 4) = 0

t = –1, –3, 4

Points are (at2 , 2at) i.e. (1, – 2), (9, – 6), (16, 8)

Centroid is (1 + 9 + 16/3 , -2 - 6 + 8/3)

= (26/3, 0)