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# 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

## 1 Answers

one year ago
Dear Jyoti

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

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