Question

Find the equation of circle whose diameter is the line joining the points $(0,-1)$ and $(2,3)$. Find also the intercept made by it on the axis of x .

Answer 1

$x(x-2)+(y+1)(y-3)=0$
or $x^2+y^2-2x-2y-3=0;$
$\therefore g=-1,f=-1,c=-3.$
Intercept on x-axis $=2\sqrt{(g^2-c)}=2\sqrt{1+3}=4.$