Equation of pair of tangents drawn from $(4, 3)$ to the circle $x^{2} + y^{2} = 4$ is

5 x^{2} + 12 y^{2} + 24 x y - 32 x + 24 y - 100 = 0

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5 x^{2} + 12 y^{2} - 24 x y + 32 x + 24 y - 100 = 0

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5 x^{2} + 12 y^{2} - 24 x y - 32 x + 24 y + 100 = 0

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5 x^{2} + 12 y^{2} + 24 x y + 16 x + 24 y - 100 = 0

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Solution

The correct option is B $5 x^{2} + 12 y^{2} - 24 x y + 32 x + 24 y - 100 = 0$
$S : x^{2} + y^{2} - 4$
$S_{1} : 4^{2} + 3^{2} - 4 = 21$
$T : 4 x + 3 y - 4$
Equation of pair of tangents is
$S S_{1} = T^{2}$
$\Rightarrow 21 (x^{2} + y^{2} - 4) = (4 x + 3 y - 4)^{2}$
$\Rightarrow 21 x^{2} + 21 y^{2} - 84 = 16 x^{2} + 9 y^{2} + 16 + 24 x y - 24 y - 32 x$
$\Rightarrow 5 x^{2} + 12 y^{2} - 24 x y + 32 x + 24 y - 100 = 0$

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