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Question

# The angle between a pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13cos2α=0 is 2α. The equation of the locus of the point P is

A

x2+y2+4x6y+4=0

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B

x2+y2+4x6y9=0

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C

x2+y2+4x6y4=0

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D

x2+y2+4x6y+9=0

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Solution

## The correct option is D x2+y2+4x−6y+9=0 Let PA and PB be the tangents drawn from the point P(h, k) to the given circle with centre C(-2, 3). So, that ∠APB=2α and ∠APC=∠CPB=α∠PAC=∠PBC=90∘From triangle PCA,⇒sinα=CACP and CA=√4+9−(9sin2α+13cos2α)=2sinα⇒CP=2.⇒4=h2+k2+4h−6k+13. The locus of P(h, k) is x2+y2+4x−6y+9=0

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