Question

Find the centre and radius of the circle x2 + y2 - 2x - 2y = 0​

Answer 1

Given Equation

$x^2+y^2-2x-2y$

$=(x^2-2x+1)+(y^2-2y+1)-2$

$=(x-1)^2+(y-1)^2-2$

$\therefore (x-1)^2+(y-1)^2=2$

Application of Distance Formula

$\sqrt{(x-1)^2+(y-1)^2} =\sqrt{2}$

→ The distance from $(x,y)$ and $(1,1)$ is $\sqrt{2}$. [Distance Formula]

Thus, this equation forms a circle with center $(1,1)$ and radius of $\sqrt{2}$.