Step 1

Radius \(\displaystyle{y}={\frac{{{1}}}{{{2}}}}{x}\) distance between points on diameter.

Points on diameter are (2,-7) and (5,-3)

So distance between \(\displaystyle{\left({x}_{{{1}}},{y}_{{{1}}}\right)}\) and \(\displaystyle{\left({x}_{{{2}}},{y}_{{{2}}}\right)}\) is

\(\displaystyle=\sqrt{{{\left({x}_{{{2}}}-{x}_{{{1}}}\right)}^{{{2}}}+{\left({y}_{{{2}}}-{y}_{{{1}}}\right)}^{{{2}}}}}\)

Step 2

So distance between (2,-7) and (5,-3) so

That \(\displaystyle=\sqrt{{{\left({5}-{2}\right)}^{{{2}}}+{\left(-{3}+{7}\right)}^{{{2}}}}}\)

\(\displaystyle=\sqrt{{{9}+{16}}}\)

\(\displaystyle=\sqrt{{{25}}}\)

\(\displaystyle={5}\)

So radius of circle \(\displaystyle={\frac{{{1}}}{{{2}}}}{x}{5}={25}\)

Radius \(\displaystyle{y}={\frac{{{1}}}{{{2}}}}{x}\) distance between points on diameter.

Points on diameter are (2,-7) and (5,-3)

So distance between \(\displaystyle{\left({x}_{{{1}}},{y}_{{{1}}}\right)}\) and \(\displaystyle{\left({x}_{{{2}}},{y}_{{{2}}}\right)}\) is

\(\displaystyle=\sqrt{{{\left({x}_{{{2}}}-{x}_{{{1}}}\right)}^{{{2}}}+{\left({y}_{{{2}}}-{y}_{{{1}}}\right)}^{{{2}}}}}\)

Step 2

So distance between (2,-7) and (5,-3) so

That \(\displaystyle=\sqrt{{{\left({5}-{2}\right)}^{{{2}}}+{\left(-{3}+{7}\right)}^{{{2}}}}}\)

\(\displaystyle=\sqrt{{{9}+{16}}}\)

\(\displaystyle=\sqrt{{{25}}}\)

\(\displaystyle={5}\)

So radius of circle \(\displaystyle={\frac{{{1}}}{{{2}}}}{x}{5}={25}\)