[Math] Find the equation of the circle which passes through the origin and cuts off

analytic geometrycirclesgeometry

Find the equation of the circle which passes through the origin and cuts off intercepts $3$ and $4$ from the positive parts of the axes respectively.

My Attempt,

The circle cuts the axis of $X$ at $(3,0)$ and the axis of $Y$ at $(0,4)$. Let $r$ be the radius of the circle. Since the circle passes through the origin,
$$r=\sqrt {h^2+k^2}$$,

Where, $(h,k)$ are the co ordinates of the centre of the circle.

Best Answer

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

Now it passes through $(0,0);(3,0);(0,4)$

We have three unknowns with there conditions, right?