Question

Find the equation of the circle with the center $(1,1)$ and radius.$(r) = √2.$

Answer 1

The equation of a circle with a center $(h, k)$and radius $r$ is given as $(x - h)^2 + (y -k)^2 = r^2$

It is given that the center $(h, k) = (1, 1)$ and radius $(r) =√2.$

Therefore, the equation of the circle is

$(x-1)^2+ (y-1)^2= (√2)^2$

$⇒ x^2-2x + 1 + y^2-2y + 1 = (√2)^2$

$⇒ x^2-2x+y^2-2y +2 -2= 0$

$⇒ x^2+ y^2-2x-2y = 0$ (Ans.)