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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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