Mathematics - Circle Question with Solution | TestHub

Since circle touches the x-axis at$\left(3,\mathrm{ }0\right),$hence centre can be taken as$\left(3,\mathrm{\alpha }\right)$and radius$=\left|\mathrm{\alpha }\right|$
Since y-intercept is 8, by applying Pythagorean theorem
$3^2+4^2={\alpha }^2\Rightarrow \alpha =5,-5$
Hence two circles are possible
${\left(x-3\right)}^2+{\left(y-5\right)}^2=25$and${\left(x-3\right)}^2+{\left(y+5\right)}^2=25.$
Clearly$(3,\mathrm{ }10)$satisfies the given equation of circle.