Consider the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1,\]where $a > b.$ As a function of $a$ and $b,$ find the radius of the smallest circle that contains the ellipse, is centered on the $y$-axis, and which intersects the ellipse only at $(0,b).$

Guest Feb 27, 2021