[Math] Equation of The Circle Tangent to Each Axis and Passing Through a Point

Question

Find the equation of the circle touching each axis and passing through $(2,1)$

My Attempt:

Since the circle touches both axes, the x-coordinate of the center = y-coordinate of the center = radius. If $h$, $k$ and $r$ are the x-coordinate, y-coordinate and radius then
$$h=k=r.$$

Answer 1

The equation of your circle is then $(x-r)^2+(y-r)^2=r^2$. Plug in $x=2,y=1$ and solve for $r$.