Question

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

Answer 1

Answer:
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

Answer 2

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

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 .