Find the equation of the circle which passes through origin and cuts off the intercepts - 2 and 3 over the x…

Equation of circle $=$ $x^2+y^2+2gx+2fy+c=0$ which passes through $\left(0,0\right),\left(-2,0\right),\left(0,3\right)$

When it passes through $\left(0,0\right)$, then $c=0$

When it passes through $\left(-2,0\right)$, then $4-4g=0\Rightarrow g=1$

When it passes through $\left(0,3\right)$, then $9+6f=0\Rightarrow f=\frac{-3}{2}$

Hence, the required equation of circle is $x^2+y^2+2x-3y=0$.