Question

Find the equation of a circle which passes through origin and cuts off intercepts $-2$ and $3$ from the axes.

Answer 1

Let the circle be $x^2+y^2+2gx+2fy+c=0$

$\because$ It passes through origin, $c=0$

$\Rightarrow x^2+y^2+2gx+2fy=0$

When, $y=0,x=-2$

$\Rightarrow 4-4g=0$

$\Rightarrow g=1$

When $x=0,y=3$

$\Rightarrow 0+9+0+6f=0$

$\Rightarrow f=\frac{-3}{2}$

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