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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

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

Grade:Upto college level

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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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sunny redu
24 Points
7 years ago
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

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