Question

Find the equation of the circle when the end points of a diameter are $A(2,3)$ and $B(3,5)$

Answer 1

Using diameter form,the equation of the circle having $A(2,3)$ and $B(3,5)$ as the end points of a diameter is

$(x-2)(x-3)+(y-3)(y-5)=0$

$\Rightarrow x^2-2x-3x+6+y^2-3y-5y+15=0$

$\Rightarrow x^2+y^2-5x-8y+21=0$ is the required equation of the circle.