Question

Find the equation of the circle drawn on the line joining the points $(-1,-3)$ and $(2,5)$ as diameter.

Answer 1

We know that, the equation of the circle drawn on the straight line joining two given point $(x_1,y_1)$ and $(x_2,y_2)$ as diameter is $(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$

Given points are $(-1,-3),(2,5)$.

Thus the equation is $(x+1)(x-2)+(y+3)(y-5)=0$

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

$\Rightarrow x^2+y^2-x-2y-17=0$ is the required equation of the circle.