Question

Write the standard form the equation for the circle that passes through the points (-9,-16),(-9,32), and (22,15)? then identify the center and radius?

Answer 1

`(x+9)^2=(y-8)^2=576`
Center: `(-9,8)`
Radius: `24`

Explanation:

We need to know the center and radius of the circle before we can write the equation. We only need to focus on `(-9,-16)` and `(-9,32)` because the other coordinate will confuse us and give us unnecessary work.
First, notice how we have the same x-value and two y-values in our equation. That means we have a diameter! As you know, a diameter is two times the radius:

`16+32=2r`
`48=2r`
`24=r`

Next, let's find the center. The center is the midpoint between our two coordinates, so let's just subtract our radius from `(-9,32)`:

`(-9,32-24) = (-9,8)`

All we have to do next is plug our values into the standard formula for a circle:

`(x-h)^2+(y-k)^2=r^2`
`(x-(-9))^2+(y-8)^2=24^2`
`(x+9)^2=(y-8)^2=576`