Mathematics - Circle Question with Solution | TestHub

Centre $(\mathrm{a},0)$
$\mathrm{r}=\left|\frac{\mathrm{a}-0-3}{\sqrt{2}}\right|$
$\mathrm{circle}(x-a{)}^2+y^2={\left(\frac{a-3}{\sqrt{2}}\right)}^2$
passes through $(-9,4)$
$2\left(a^2+18a+81+16\right)=\left(a^2-6a+9\right)$
${\mathrm{a}}^2+42\mathrm{a}+185=0$
$(a+37)(a+5)=0$
$\Rightarrow a=-37,-5$
$r_1=\left|\frac{-37-3}{\sqrt{2}}\right|=20\sqrt{2}$
${\mathrm{r}}_2=\left|\frac{-5-3}{\sqrt{2}}\right|=4\sqrt{2}$
$\left|r_1^2-r_2^2\right|=|800-32|=768$