Correct answer is : 9
\((x-h)^{2}+(y-k)^{2}=h^{2}+k^{2}\)
\(x^{2}+y^{2}-2 h x-2 k y=0\)
\(\because\) passes through \((1,0)\)
\(\Rightarrow 1+0-2 \mathrm{h}=0\)
\(\Rightarrow \mathrm{h}=1 / 2\)
\(\because \ \mathrm{OC}=\frac{\mathrm{OP}}{2}\)
\(\sqrt{\left(\frac{1}{2}\right)^{2}+\mathrm{k}^{2}}=\frac{3}{2}\)
\(\frac{1}{4}+\mathrm{k}^{2}=\frac{9}{4}\)
\(\mathrm{k}^{2}=2\)
\(\mathrm{k}= \pm \sqrt{2}\)
\(\therefore\) Possible coordinate of
\(\mathrm{c}(\mathrm{h}, \mathrm{k})\left(\frac{1}{2}, \sqrt{2}\right)\left(\frac{1}{2},-\sqrt{2}\right)\)
\(4\left(\mathrm{~h}^{2}+\mathrm{k}^{2}\right)=4\left(\frac{1}{4}+2\right)=4\left(\frac{9}{4}\right)=9\)
