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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

1 Answer

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Best answer

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

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