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If two tangents to the parabola y2 =4ax form a point P make angles θ1 and θ2 with the axis of parabola then find the locus of point P such that tan θ1 and tan θ2= alpha

If two tangents to the parabola y2=4ax form a point P make angles θ1 and θ2 with the axis of parabola then find the locus of point P such that tan θ1 and tan θ2= alpha
 

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
Let the digression to parabola at (at12,2at1) is yt1 =x+at12 
also digression at (at22,2at2) is yt2 =x+at22 
these digression meet at point P 
so point p is 
{at1t2,a(t1 +t2)} 
likewise tan Θ1 =1/t1 
tanθ 2 =1/t2 
what's more, tan(θ1 + Θ2) = tan pi/2 
illuminating 
so t1t2 =1 
locus of point p 
x=at1t2 

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