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If the chord of contact of tangents from a point P(h,k) to the circle x 2 + y 2 = a 2 touches the circle x 2 + (y-a) 2 = a 2 , then locus of P is

If the chord of contact of tangents from a point P(h,k) to the circle x2 + y2 = a2  touches the circle  x2  + (y-a)2 = a2 , then locus of P is 

Grade:11

1 Answers

JOEL JOHNSON
35 Points
5 years ago
Equation of chord of contact from p(h,k) to x2+ y= ais xh + yk = a2  this line touches (x)2 + (y-a)2 = asubstituting x= (a2-yk)/h from the first equation, we get a quadratic in y.The line touches the second circle in only one point, so discriminant should be equal to zero. We get,      h2+ 2a2k2 + 2ak -a2= 0 , therefore the required locus is x2 +2a2y2 +2ay -a2=0

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