Question

Identify the center and the radius of a circle with equation (x-4)^2+(y+2)^2=9

Answer 1

Center at (4,-2); radius: 3

Explanation:

Answer 2

center:(4,-2)

Radius: 3 units

Explanation:

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

The given equation is
`(x-4)^2+(y+2)^2=9`.

We compare to the standard equation of the circle to get;

`x-h=x-4`

`\Rightarrow -h=-4`

`\Rightarrow h=4`

and

`y-k=y+2`

`\Rightarrow -k=2`

`\Rightarrow k=-2`

Hence the center of the circle is (4,-2).

Also, we have
`r^2=9`

Therefore
`r=√(9)`

`r=3` units.