Question

A circle is drawn whose centre is on the $x-axis$ and it touches the $y-axis.$ If no part of the circle lies outside the parabola $y^{2}=8x,$ then the maximum possible radius of the circle is

Answer 1

Let equation of circle is $\left(x - r\right)^{2}+y^{2}=r^{2}$
Solving it with $y^{2}=8x,$ we get,
$x^{2}-2rx+r^{2}+8x=r^{2}\Rightarrow x=0$ or $x=2r-8$
$\Rightarrow r_{m a x i m u m}=4$