The equation of the chord of contact of tangents drawn from the point $(2, - 3)$ to the circle $x^{2} + y^{2} + 4 x - 6 y - 12 = 0$ is

4 x - 6 y - 17 = 0

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4 x + 6 y - 17 = 0

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4 x + 6 y + 17 = 0

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None of these

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Solution

The correct option is A $4 x - 6 y - 17 = 0$
The equation of the chord of contact of tangents drawn from external point to the circle $S$ is equal to the equation of tangent at that point.
$∴$ Required equation is
$x \times 2 - y \times 3 + 4 (\frac{x + 2}{2}) - 6 (\frac{y - 3}{2}) - 12 = 0$
$\Rightarrow 2 x - 3 y + 2 x + 4 - 3 y - 9 - 12 = 0$
$\Rightarrow 4 x - 6 y - 17 = 0$ .

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4^{th}

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