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from any arbitrary point P on y=cos x , tangents PA and PB are drawn to a circle which passes through the points (1,0),(3,0) and touches the circle x 2 +y 2 -2x-8=0 and have its centre in first quadrant. find the locus of circumcentre of triangle PAB

from any arbitrary point P  on y=cos x , tangents PA and PB are drawn to a circle which passes through the  points (1,0),(3,0) and touches the circle x2+y2-2x-8=0 and have its centre in first quadrant. find the locus of circumcentre of triangle PAB

Grade:11

1 Answers

Prakash
21 Points
6 years ago
Equation of the family of circle passing through the given point and tangent to the given circle is x^2+y^2-4x +Ky+3=0 now apply the condition c1c2=r1-r2 we get k=√5 now the circumcenter of the triangle pab is the mid point of p and the cente of theabove circle so its locus will be cos(2x-2)+√5/2=2y

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