Question

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

Answer 1

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

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

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

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