If the ordinates of points P and Q on the parabola y^2=12 x are in the ratio 1: 2 , then the locus of the point of intersection of the normals to the parabola at P and Q is

Step-by-step solution

Given, t₁ t₂ =2 Let t₂=t t₁=2 t Point of intersection of normals at t₁ and t₂ is aligned & (2 a+a (t₁^2+t₂^2+t₁ t₂ ),-a t₁ t₂ (t₁+t₂ ) . & (2 a+a (4 t^2+t^2+2 t^2 ),-2 a t^2 3 t ) (2 a+7 a t^2,-6 a t^3 ) & x=2 a+7 a t^2, y=-6 a t^3 & x-2 a=7 a t^2, y=-6 a t^3 & a=3 x-6=21 t^2, y=-18 t^3 aligned Eliminating t we get, y+18 ( x-6 21 )^ 3 / 2 =0 .