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Vanya Saxena Grade: Upto college level
`        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`
8 years ago

147 Points
```										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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```
8 years ago
sunny redu
24 Points
```										as in the given question the two tangents are perpendicular  and the locus of perpendicular tangents is director circle and in case of parabola director circle is directrix and in the question directrix is x=a which is is required locus
```
6 months ago
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