If two tangents to the parabola y^2=4ax from a point p makes angles theta 1 and theta 2 with the axis of the parabola ,then find the locus of p in each of the following cases. Theta1+theta2=alpha (constant ) and theta 1 + theta 2=π\2

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)}

 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