Final answer:
The center of the equation is (3/2, -2) and the radius is √45/2.
Step-by-step explanation:
To find the center and radius of the equation 4x² + 4y² - 12x + 16y - 5, we need to rewrite it in the standard form of a circle equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
We can rewrite the given equation as (x² - 3x) + (y² + 4y) = 5.
Completing the square for both x and y, we get (x - 3/2)² - 9/4 + (y + 2)² - 4 = 5.
Simplifying further, we have (x - 3/2)² + (y + 2)² = 9/4 + 9 = 9/4 + 36/4 = 45/4.
Thus, the center is (3/2, -2) and the radius is √(45/4) = √45/2.