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

Answer 1

Answer: (C)

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

Given equation of circle is
$S:$ $x^2+y^2+20(x+y)+20=0$.
Comparing with general eqn of circle, we get
$g=10,f=10,c=20$
Equation of circle at $(0,0)$ is
$S_1:20$
Equation of tangent to circle at $(0,0)$
$T:10x+10y+20$
Now, equation of pair of tangents drawn from $(0,0)$ to circle is
$S{S}_1=T^2$

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

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