Question

For the equation x^2 + y^2 - 4x + 2y = b, the radius is 7. What is the center and the value of b?

A) Center: (2, -1); b = 24
B) Center: (2, -1); b = -24
C) Center: (4, -2); b = 24
D) Center: (4, -2); b = -24

Answer 1

The center of the circle is (2, -1) and the value of b is 45.

Step-by-step explanation:

The equation of the circle can be rewritten as (x - 2)² + (y + 1)² = b + 4.

Since the radius is 7, the equation becomes (x - 2)² + (y + 1)² = 7² = 49.

Comparing this equation with the standard form of a circle, (x - h)² + (y - k)² = r², we can conclude that the center is at (h, k) = (2, -1) and the value of b is b = 49 - 4 = 45.