Question

How do you find the center and radius of `(x-2)^2+(y+3)^2=4`?

Answer 1

In order to find the center and radius, we must first understand how a standard circle equation is written.

Explanation:

The standard form for a circle is written as:

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

where `h` is the x-value of the origin, `k` is the y-value of the origin, and `r` is the radius of the circle. Firstly, let's take out our origin from the equation. A way I like to imagine the origin is to switch the sign that `h` and `k` have. Therefore, our origin is `(2,-3)`. Let's plug in our origin back into the equation to make sure:

`(x-(2))^2+(y-(-3))^2=4`
`(x-2)^2+(y+3)^2=4`

For our radius, we take the square root of `r^2` value:

`r^2=4`
`r=2`
Note that `-2` is not an answer because it is not possible to have a negative distance in a graph.