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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

6 years ago


Answers : (1)


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


so t1t2 =1

locus of point p



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