Question

A pair of tangents are drawn from the origin to the circle $x^2 + y^2+ 20 (x + y) + 20 = 0$, then the equation of the pair of tangent are

• A. $x^2 + y^2 - 5xy = 0$
• B. $x^2 + y^2 + 2x + y = 0$
• C. $x^2 + y^2 - xy + 7 = 0$
• D. $2x^2 + 2y^2 + 5xy = 0$

Answer 1

Answer: (D)

$2x^2 + 2y^2 + 5xy = 0$

Answer 2

Equation of pair of tangents is given by $S S_{1}=T^{2}$
or $S=x^{2}+y^{2}+20(x +y)+20, S_{1}=20$,
$T=10(x +y)+20=0$
$\therefore S S_{1}=T^{2}$
$\Rightarrow 20\left(x^{2}+y^{2}+20(x +y)+20\right)=10^{2}$
$(x+y+2) 2$
$\Rightarrow 4 x^{2}+4 y^{2}+10 x y=0$
$\Rightarrow 2 x^{2}+2 y^{2}+5 x y=0$