The tangents to the parabola y^2=4 a x from an external point P make angles ₁ and ₂ with the axis of the parabola. Such that ₁+ ₂=b , where b is constant. Then P lies on

Step-by-step solution

Here, P is intersecting point of tangents at gathered A (a t₁^2, 2 a t₁ ) and B (a t₂^2, 2 a t₂ ) P (a t₁ t₂ a (t₁ t₂ ) . gathered Slope of line P A = ₁= 2 a t₁-a t₁-a t₂ a t₁^2-a t₁ t₂ = a (t₁-t₂ ) a t₁ (t₁-t₂ ) = 1 t₁ Similarly, Slope of line P B= ₂= 2 a t₂-a t₁-a t₂ a t₂^2-a t₁ t₂ = a (t₂-t₁ ) a t₂ (t₂-t₁ ) = 1 t₂ According to the question, aligned & ₁+ ₂=b & 1 t₁ + 1 t₂ =b & t₂+t₁=b t₁ t₂ & y a = b x a [ x=a t₁ t₂, y=a (t₁+t₂ ) ] & y=b x aligned P lies on the line y=b x