Question

What is center of the circle given by its equation (x-2)^2 + (y+4)^2=6?

Answer 1

(2,-4) is the center

Explanation:

The standard form of a circle is
`(x-h)^2+(y-k)^2=r^2` where (h,k) is the center and r is the radius.

So if you compare

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

and

`(x-2)^2+(y+4)^2=r^2`,

you should see that

`h=2`

`-k=4` which implies
`k=-4`

`r^2=6` which implies
`r=√(6)`.

So the center is (h,k)=(2,-4).

The radius is
`√(6)`.