Find the length of tangents drawn from the point $(3, - 4)$ to the circle $2 x^{2} + 2 y^{2} - 7 x - 9 y - 13 = 0$

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Solution

$x^{2} + y^{2} - \frac{7}{2} x - \frac{9}{2} y - 13 = 0$
$(3, - 4)$
Length of tangents $\to \sqrt{3^{2} + 4^{2} - \frac{7}{2} .3 \frac{- 9}{2} (- 4) - 13}$
$\Rightarrow \sqrt{9 + 16 - \frac{21}{2} + \frac{36}{2} - 13} \Rightarrow \sqrt{25 + 18 - 13 - \frac{21}{2}}$
$\Rightarrow \sqrt{\frac{30 - 21}{2}} = \sqrt{\frac{39}{2}}$

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