Question

Find the equation of circle with centre $(1,2)$ and which passes through the point $(4,6)$.

Answer 1

Circle equation: $(x-a{)}^2+(y-b{)}^2=r^2$

Centre, $(1,2)$

$(x-1{)}^2+(y-2{)}^2\pm r^2$

$(4,6)$ passing

$(4-1{)}^2+(6-2{)}^2=r^2$

$\Rightarrow r^2=25$

$\Rightarrow r=5$

$\therefore$ Equation of circle$:(x-1{)}^2+(y-2{)}^2=5^2$.