Question

What is the equation of the circle with a center at `(2 ,1 )` and a radius of `2`?

Answer 1

`(x-2)^2+(y-1)^2=4`

Explanation:

The standard form of a circle with a center at `(h,k)` and a radius `r` is

`(x-h)^2+(y-k)^2=r^2`

Since the center is `(2,1)` and the radius is `2`, we know that

`{(h=2),(k=1),(r=2):}`

Thus, the equation of the circle is

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

This simplifies to be

`(x-2)^2+(y-1)^2=4`