Respuesta :

calculista

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of the circle into center radius form is equal to

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

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

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

[tex](x)^{2}+(y-4)^{2}=4^{2}[/tex]

so

the center is the point [tex](0,4)[/tex]

the radius is [tex]r=4\ units[/tex]

therefore

the graph in the attached figure

Ver imagen calculista
MrRoyal

The graph of [tex]x^2 + (y- 4)^2 =16[/tex] has a radius of 4, and its center is at (0,4)

The equation of the circle is given as:

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

Express 16 as the square of 4

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

Rewrite the equation as:

[tex](x - 0)^2 + (y- 4)^2 =4^2[/tex]

The equation of a circle is represented as:

[tex](x - a)^2 + (y- b)^2 =r^2[/tex]

Where:

Center = (a,b) = (0,4)

Radius = r = 4

Hence, the graph of [tex]x^2 + (y- 4)^2 =16[/tex] has a radius of 4, and its center is at (0,4)

Read more about circle equations at:

https://brainly.com/question/1559324