Question

How do you find the center and the radius of the circle; the graph the circle of `x^2+y^2+8x-8y-93=0`?

Answer 1

The centre is `(-4,4)` and the radius is `5sqrt(5)`

Explanation:

The standard form of a circle is `(x-h)^2 + (y-k)^2 =r^2`

To get this equation into the right form, start by grouping like terms.
`x^2 +8x +y^2 - 8y = 93`
`(x+4)^2 -16 +(y-4)^2 -16 = 93`
`(x+4)^2 +(y-4)^2 = 93 +32 = 125`

`(x+4)^2 +(y-4)^2 = (5sqrt(5))^2`

The centre is `(-4,4)` and the radius is `5sqrt(5)`