If two tangents to the parabola y²=4ax makes angle A& B with the X axis and tan²A +tan²B=c.Find the locus of the point of intersection of the tangents.

Please show how 2 solve....rates assured

i think this is simple....consider any 2 points (at₁²,2at₁) and (at₂²,2at₂) let tangents be drawn from these points....then the slope of tangent from point1 is 1/t₁=tanA and from pt2 is 1/t₂=tanB let (x,y) be the point of intersection of the tangents....then x=at₁t₂ and y=a(t₁+t₂) i am not very sure of this formula... but i think it is correct....now all u have to do is eliminate t₁ and t₂ from the given relation we have (t₁²+t₂²)/t₁².t₂² =c                 =>((t₁+t₂)²-2t₁.t₂)/(t₁.t₂)²=c  => (y/a)²-2x/a=c(x/a)² so the ans is cx²+2ax=y².....