If two tangents to the parabola y2=4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

Dear vanya saxena

tangent at parabola at (at₁²,2at₁)  is yt₁ =x+at₁²

so tangebt at (at₂²,2at₂)  is yt₂ =x+at₂²

these tangent meat at point P

so point p is

{at₁t₂,a(t₁ +t₂)}

also  tan Θ₁ =1/t1

      tanΘ ₂ =1/t2

and tan(Θ₁ + Θ₂) = tan pi/2

simplify

so t₁t₂ =1

locus of point p

x=at₁t₂

x=a

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