Find the radius of circle $C$ that touches the parabola $y= \frac 12 x^2$, at point $(2,2)$.

Question

The circle is contained in the domain $x \geq 0$ and $y \geq 0$ and the parabola equation is $y = \dfrac{1}{2}x^2$.

Answer 1

Hint: Let $(x-a)^2+(y-b)^2=b^2$ be that circle then $(2,2)$ is on the circle and the tangent at circle is equal to tangent at parabola in $(2,2)$.