Question

How do you find the center and the length of the radius of `x^2 + (y+6)^2 = 16/25`?

Answer 1

Center: `(0,-6)`
Radius: `4/5`

Explanation:

This is in the standard form of a circle:

`(x-color(blue)h)^2+(y-color(red)k)^2=color(green)r^2`

where: `(color(blue)h,color(red)k)` is the radius of the circle and `color(green)r` is the radius.

We can rewrite the original equation to match the standard form equation more clearly.

`(x-color(blue)0)^2+(y-(color(red)(-6)))^2=(color(green)(4/5))^2`

The circle has a center at `(0,-6)` and a radius length of `4/5`.