A pair of tangents are drawn from the origin to the circle $x^{2} + y^{2} + 20 (x + y) + 20 = 0$ . The equation of the pair of tangents is

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Solution

The correct option is C

Equation of pair of tangents is given by $S S_{1} = T^{2}$ .
Here $S = x^{2} + y^{2} + 20 (x + y) + 20, S_{1} = 20$

$T = 10 (x + y) + 20$

$∴ S S_{1} = T^{2}$

$\Rightarrow 20 {x^{2} + y^{2} + 20 (x + y) + 20} = 10^{2} (x + y + 2)^{2}$

$\Rightarrow 4 x^{2} + 4 y^{2} + 10 x y = 0 \Rightarrow 2 x^{2} + 2 y^{2} + 5 x y = 0$

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x^{2} + y^{2} + 20 (x + y) + 20 = 0

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