Question

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

Answer 1

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

Let $S=x^2+y^2+20(x+y)+20=\mathrm{0...}\left(1\right)$

$S_1=20...\left(2\right)$

$e{q}^n$ of the tangents is given by

$S{S}_1=T^2$

$T=10(x+y)+20...\left(3\right)$

So, from (1) & (2) & (3), we put these

values in $e{q}^n$ , we get

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

On solving, we get the $e{q}^n$ as

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