Question

Help!!! Find the center and radius of the circle with the equation (x-4)²+(y+6)²=16

Answer 1

Answer:

Center = ( 4, -6) ; radius = 4.

Step-by-step explanation:

Given : (x-4)²+(y+6)²=16.

To find :  Find the center and radius of the circle with the equation.

Solution : We have given (x-4)²+(y+6)²=16.

We can write is as (x-4)²+(y+6)²= 4².

Standard form of circle : (x – h)² + (y – k)² = r².

Where (h ,k) is center

r =  radius .

On comparing (x-4)²+(y+6)²=16 with (x – h)² + (y – k)² = r².

(h,k) = ( 4 , -6)

r = 4.

Therefore, Center = ( 4, -6) ; radius = 4.

Answer 2

Answer:

Center:  $(4,-6)$

Radius: $4$

Step-by-step explanation:

It is necessary to remember that the Equation of the circle in Center-radius form, is:

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

Where the center of the circle is at the point (h, k) and the radius is "r".

Then, given the following equation of the circle:

$(x-4)^2+(y+6)^2=16$

We can notice that it is written in Center-radius form. Then we can identify that:

$h=4\\k=-6$

Therefore the center is:

$(4,-6)$

And the radius is:

$r^2=16\\\\r=\sqrt{16}\\\\r=4$