**Correct option (B) 36**

**Explanation :**

Let P = (t_{1}^{2} , 2t_{1}) and Q = (t_{2}^{2},^{ }2t_{2}) so that, by hypothesis, we have

(2t_{1}) : (2t_{2}) = 1 : 2

⇒ t_{2} = 2t_{1} ....(1)

Let (x_{1}, y_{1}) 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 (x_{1}, y_{1}) is

36/343(x - 2)^{3} = y^{2}