The angle between the pair of tangents drawn from a point `P` to the circle `x^2+y^2+4x-6y+9sin^2alpha+13cos^2alpha=0` is `2alpha` . then the equation of the locus of the point `P` is a. `x^2+y^2+4x-6y+4=0` b. `x^2+y^2+4x-6y-9=0` c. `x^2+y^2+4x-6y-4=0` d, `x^2+y^2+4x-6y+9=0`

Explanation

To solve the problem, we need to find the equation of the locus of the point \( P \) from which the angle between the pair of tangents drawn to the given circle is \( 2\alpha \).

### Step 1: Rewrite the Circle Equation
The given equation of the circle is:
\[ x^2 + y^2 + 4x - 6y + 9\sin^2\alpha + 13\cos^2\alpha = 0 \]
We can rearrange this equation to identify the center and radius of the circle.
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