Question

The ordinates of the points P and Q of a parabola y² = 4x are in the ratio 1:2. Then the locus of the point of intersection of the normals at P and Q is

y² = k/343(x - 2)³

where the value of k is

(A)   18 

(B)   36 

(C)   54 

(D)   12

Answer 1

Correct option  (B)  36

Explanation :

Let P = (t₁² , 2t₁) and Q = (t₂², 2t₂) so that, by hypothesis, we have

(2t₁) : (2t₂) = 1 : 2

⇒ t₂ = 2t₁   ....(1)

Let (x₁, y₁) be the intersection of the normals at P and Q so that, and Eq. (1), we have

From Eqs. (1) and (2), we have

Hence, the locus of (x₁, y₁) is

36/343(x - 2)³ = y²