What is the center and radius of the circle with equation (x - 2) ^2 + (y - 5) ^2 = 100?

center (2, 5); radius = 10

center (2, - 5); radius = 100

center (-5, 2); radius = 10

center (-2, 5); radius = 100

A) Center (2, 5); radius = 10.

Step-by-step explanation:

Given : (x - 2) ² + (y - 5) ² = 100.

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

Solution : We have given (x - 2) ² + (y - 5) ² = 100.

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

Where, center = (h, k), r = radius.

On comparing (x - 2) ² + (y - 5) ² = 100 with (x - h) ² + (y - k) ² = r².

We can write (x - 2) ² + (y - 5) ² = 10².

h = 2, k = 5, r = 10.

Center (2, 5); radius = 10.

Therefore, A) Center (2, 5); radius = 10.

Center = (2,5)

Radius = 10

Choice A

To find this answer, first write the equation

(x-2) ^2 + (y-5) ^2 = 100

into

(x-2) ^2 + (y-5) ^2 = 10^2

Note how the second equation is in the form

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

We see that (h, k) = (2,5) is the center

and r = 10 is the radius