Suppose a circle passes through $(0,2)$ and $(3,5)$ and touches the $y$-axis at $Q$. If $O$ is the o

Question

Suppose a circle passes through $(0,2)$ and $(3,5)$ and touches the $y$-axis at $Q$. If $O$ is the origin, then $O Q$ is equal to

Professor PC Thomas Classes · Answer

Circle touching y-axis has $g^2 = c$. Passing through points provides equations. $OQ = \sqrt{c}$ evaluates to 3.