Mathematics - Circle Question with Solution | TestHub

The circle has centre $C(2,2)$ and radius 2. Let $\mathrm{M}(h,k)$ be the mid-point of AB and $P=(2,3)$. Since $\angle APB=90^{\circ },MP=MB$. Also $C{M}^2+M{B}^2=C{B}^2=4$. So $(h-2{)}^2+(k-2{)}^2+(h-2{)}^2+(k-3{)}^2=4$, which gives $x^2+y^2-4x-5y+\frac{17}{2}=0$. Its centre is $\left(2,\frac{5}{2}\right)$.