Question

Find the equation of the circle, the coordinates of the end points of whose diameter are $(-1,2)$ and $(4,-3)$

Answer 1

We know that the equation of the circle described on the line segment joining $(x_1,y_1)and(x_2,y_2)$ as a diameter is $(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$
Here $x_1=-1,x_2=4,y_1=2and{y}_2=-3$
So the equation of the required circle is
$(x+1)(x-4)+(y-2)(y+3)=0$ $\Rightarrow$ $x^2+y^2-3x+y-10=0$