Question

If a circle passes through the point $A(1,0),$ $B(5,0)$ and touches $y-$axis at $C(0,h),$ then the value of $h^2$ is

Answer 1

Here, point $D$ is the mid-point of $AB$
So, the coordinates of $D$ are $(\frac{5+1}{2},0)\equiv (3,0)$
Hence, the centre of the circle is $O(3,h)$
Now, from $△ODA$
$O{A}^2=O{D}^2+A{D}^2$
$\Rightarrow 3^2=h^2+2^2$
$\Rightarrow h^2=5$