The angle between a pair of tangents from a point P to the circe `x^2 + y^2+ 4 x-6y + 9 sin2 alpha + 13 cos^2 alpha =0` is `2alpha`. Find the equation of the locus of the point P.

Options

A. a.`x^2+y^2+4x-6y+4=0`
B. b. `x^2+y^2+4x-6y-9=0`
C. c. `x^2+y^2+4x-6y-4=0`
D. d. `x^2+y^2+4x-6y+9=0`

Explanation

let the coordinates of P are`(h,k)`

the angle made by P to the tangents is `2alpha`

the centre of the circle is C`(-2,3)`

so, `r= sqrt(4+9-9sin alpha - 13cos^2 alpha)`

`r= sqrt(4+9cos^2 alpha-13cos^ alpha) `

`= sqrt(4-4cos^2 alpha)`

`=sqrt(4(sin^2 alpha))`

`=2sin alpha`

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