2022 TWO(e)

The curve with the equation $(y-5{)}^2=16(x-2)$ has a tangent of gradient 1 at point P.

This tangent intersects the $x$ and $y$ axes at points R and S respectively.

Prove that the length RS is $7\sqrt{2}$.

*You must use calculus and show any derivatives that you need to find when solving this problem.*