Question

Find equation of circle passing through $(2,2)$ and its center is $(4,5)$

Answer 1

Center of circle is $(4,5)$

Equation of circle is $(x-4{)}^2+(y-5{)}^2=r^2$

It passes through $(2,2)$

$⟹(2-4{)}^2+(2-5{)}^2=r^2$

$\Rightarrow 2^2+3^2=r^2$

$\Rightarrow 4+9=r^2$

$\Rightarrow r^2=13$

Equation of circle is $(x-4{)}^2+(y-5{)}^2=13$

$\Rightarrow x^2-8x+16+y^2-10y+25=13$

$\Rightarrow x^2+y^2-8x-10y+28=0$