Question

What is the equation of a circle that has radius `r` centred on the origin?

Answer 1

`x^2 + y^2 = r^2`

Explanation:

The standard equation of a circle with centre `(a,b)` and radius `r` is:

`(x-a)^2 + (y-b)^2 = r^2`

Thus the equation we seek with centre `(a,b)=(0,0)` is:

`(x-0)^2 + (y-0)^2 = r^2`

i.e.

`x^2 + y^2 = r^2`