Length of chord of contact drawn from $(0, 0)$ to the circle $x^{2} + y^{2} + 16 x + 12 y + 8 = 0$ is $0.8 \sqrt{k}$ units, then $k =$

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Solution

Length of chord of contact $= \frac{2 L r}{\sqrt{L^{2} + r^{2}}}$
$∵ r = \sqrt{92} = 2 \sqrt{23}$ units
$L = \sqrt{S_{1}} = 2 \sqrt{2}$ units
$∴$ Length of chord of contact
$0.8 \sqrt{k} = \frac{2 \times 2 \sqrt{2} \times 2 \sqrt{23}}{\sqrt{8 + 92}}$
$\Rightarrow 0.8 \sqrt{k} = \frac{8 \sqrt{46}}{10} = 0.8 \sqrt{46} ∴ k = 46$

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