Question

Find the center and radius when x^2+y^2+4x-4y=17

Answer 1

Center: (-2,2)

Radius:5

Explanation:

The first step in this problem is to complete the square and to find the equation of this circle in standard form.

`x^2+y^2+4x-4y=17` can be rearranged to be:

`x^2+4x+y^2-4y=17`

Now, you can begin to complete the square with both the x and the y:

`(x^2+4x+4)-4+(y^2-4y+4)-4=17`

Adding 8 to both sides and finishing the squares:

`(x+2)^2+(y-2)^2=25`
`(x+2)^2+(y-2)^2=25`

The coordinates of the center of the circle are (-2,2), and the radius is
`√(25)=5`. Hope this helps!

Answer 2

the center is (-2,2) and the radius is 5