Answer:
C. center: (7/2, -3/2); radius: sqrt(74)/2
Explanation:
x^2 + y^2 - 7x + 3y - 4 = 0
We can put the equation in standard form by completing the square in x and in y.
x^2 - 7x + ___ + y^2 + 3y + ___ = 4 + ___ + ___
x^2 - 7x + (7/2)^2 + y^2 + 3y + (3/2)^2 = 4 + (7/2)^2 + (3/2)^2
(x - 7/2)^2 + (y + 3/2)^2 = 16/4 + 49/4 + 9/4
(x - 7/2)^2 + (y + 3/2)^2 = 74/4
(x - 7/2)^2 + (y + 3/2)^2 = (sqrt(74)/2)^2
Answer: center: (7/2, -3/2); radius: sqrt(74)/2