Finding the radius of a circle?

Question

Determine the center and radius of each circle.

y^2= 25 - (x+1)^2

(x - 2)^2 = 8 - (y +2)^2

Could you show me the steps on how to solve it. I don't understand thanks.

Answer 1

The idea is to get the equation into the standard form of a circle which

is: (x - h)² + (y - k)² = r²

where h and k are the x and y coordinates of the center of the circle and r is the radius. Then you can readily recognize the center and the radius.

(y)²+ (x + 1)² = 25

(y - 0)² + (x - (-1))² = 25

(x - (-1))² + (y - 0)² = 25

Answer: center = (-1,0) and the radius is 5

(x - 2)² = 8 - (y + 2)²

(x - 2)² + (y + 2)² = 8

(x - 2)² + (y - (-2))² = 8

Answer: center = (2,-2), radius = √8 = 2√2