Question

Find the equation of a circle, the end points of one of whose diameters are A (2, -3) and B(-3, 5).

Answer 1

We know that the equation of a circle, the end points of one of whose diameters are $x_1,y_1$ and $x_2,y_2$, is given by

$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0.$

Here, $x_1=2,y_1=-3$ and $x_2=-3,y_2=5.$

$\therefore$ the required equation of the circle is

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

$\Rightarrow x^2+y^2+x-2y-21=0.$