Question

Find the equation of the circle with end points of the diameter as $(2,-1)$ and $(3,2)$.

Answer 1

The equation of circle with ends of diameter is $(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$ ,where, $(x_1,y_1)$ and$(x_2,y_2)$ are ends of diameter.

Here, $(x_1,y_1)\equiv (2,-1)$ and $(x_2,y_2)\equiv (3,2)$

Thus equation of circle :- $(x-2)(x-3)+(y-(-1\left)\right)(y-2)=0\Rightarrow x^2-5x+6+y^2-y-2=0\Rightarrow x^2+y^2-5x-y+4=0$