Question

Find the circumcircle of the triangle formed by the lines $x=0,x+y+3=0andx-y+1=0$

Answer 1

Slope of $x-y+1=0$ is $1$ and slope of $x+y+3=0$ is $-1$

So, $x-y+1=0$ and $x+y+3=0$ are perpendicular to each other

$(\because \text{product of slopes}=-1)$

$\therefore ABC$ is right angled triangle.

$AC$ is diameter of circumcircle.

$\therefore$ Equation of circle is $(x-0)(x-0)+(y-1)(y-3)=0$

$\therefore x^2+y^2+2y-3=0$