Respuesta :

luisejr77

Answer:

Center:  [tex](4,-6)[/tex]

Radius: [tex]4[/tex]

Step-by-step explanation:

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

[tex](x -h)^2 + (y-k)^2 = r^2[/tex]

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:

[tex](x-4)^2+(y+6)^2=16[/tex]

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

[tex]h=4\\k=-6[/tex]

Therefore the center is:

[tex](4,-6)[/tex]

And the radius is:

[tex]r^2=16\\\\r=\sqrt{16}\\\\r=4[/tex]

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.

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