Finding The Smallest Circle Through a Point and Centre On a Line
The equation of circle, ${{C}_{1}}$, is ${{x}^{2}}+{{y}^{2}}-4x-2y-20=0$.
(i)
Find the centre and the radius of the circle.
(ii)
Show that the point $P\left( -2,4 \right)$ is on the circle.
(iii)
Find the equation of the smallest circle, ${{C}_{2}}$, passing through $P$ and having its centre on the line $x+5y=2$.
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