Question

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.

• A. $x ^ { 2 } + y ^ { 2 } + 10 x y = 0$
• B. $x ^ { 2 } + y ^ { 2 } + 5 x y = 0$
• C. $2 x ^ { 2 } + 2 y ^ { 2 } + 5 x y = 0$
• D. $2 x ^ { 2 } + 2 y ^ { 2 } - 5 x y = 0$

Answer 1

Answer: (C)

$2 x ^ { 2 } + 2 y ^ { 2 } + 5 x y = 0$

Answer 2

Equation of pair of tangents is given by $S S _ { 1 } = T ^ { 2 }$.

Here $S = x ^ { 2 } + y ^ { 2 } + 20 ( x + y ) + 20 , S _ { 1 } = 20$

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

$\therefore S S _ { 1 } = T ^ { 2 }$

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

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