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)