Sketching graphs of circles.

Question

A circle graph function is in the form of $x^2 + y^2 = r^2$

If I am asked to graph $(x-2)^2 + (y - 1)^2 = 4$, do I have to solve for x and y to graph first?

Answer 1

No, you can graph it immediately. This is a circle with centre $(2,1)$ and radius $2$.

Answer 2

Hint: $x^2 + y^2 = r^2$ is the equation of a circle with centre at $(0,0)$. $(x-2)^2 + (y-1)^2 = 4$ is also the equation of a circle, but its centre is not at $(0,0)$. Where do you suppose its centre is?

Answer 3

$(x-a)^2+(y-b)^2=r^2$ is a circle with centre $(a,b)$ and radius $r$.