4. Determine the center and radius of each circle.

a. 3x2^+3y^2=75

b. 2 (x+1) ^2+2 (y+2) ^2=10

c. 4 (x-2) ^2+4 (y-9) ^2-64=0

a) Center (0,0) and radius 5b) Center (-1,-2) and radius 2.236c) Center (2,9) and radius 4

Step-by-step explanation:

Equation of circle with (h, k) as center and radius r is given by,

(x-h) ² + (y-k) ² = r²

a) 3x²+3y²=75

Dividing by 3

x²+y²=25

(x-0) ² + (y-0) ² = 5²

Center (0,0) and radius 5

b) 2 (x+1) ²+2 (y+2) ²=10

Dividing by 2

(x+1) ² + (y+2) ²=5

(x - (-1)) ² + (y - (-2)) ² = 2.236²

Center (-1,-2) and radius 2.236

c) 4 (x-2) ²+4 (y-9) ²-64=0

4 (x-2) ²+4 (y-9) ² = 64

Dividing by 4

(x-2) ² + (y-9) ² = 16

(x-2) ² + (y-9) ² = 4²

Center (2,9) and radius 4