Final answer:
The center and radius are found by completing the square for the x and y terms in the general circle equation. After completing the square, the equation (x - 1)² + (y - 1.5)² = 7.25 suggests that the center is at (1, 1.5) with a radius of √7.25 or approximately 2.69, which does not match any of the provided options.
Step-by-step explanation:
To find the center and radius of a circle given in the general form x² + y² - 2x - 3y - 4 = 0, we need to complete the square for both the x and y terms. This process will allow us to write the equation in the standard form of a circle, which is (x - h)² + (y - k)² = r², where (h, k) represents the center and r is the radius.
First, we group the x and y terms and complete the square for each group:
- (x² - 2x) can be written as (x - 1)² - 1², adding and subtracting 1 inside the parenthesis.
- (y² - 3y) can be written as (y - 1.5)² - 1.5², adding and subtracting 2.25 inside the parenthesis.
Now include these additional numbers on the left-hand side of the equation:
(x - 1)² + (y - 1.5)² - 1 - 2.25 - 4 = 0
Combine like terms on the left to get the constants on the right side:
(x - 1)² + (y - 1.5)² = 7.25
To find the radius, take the square root of the right side:
r = √7.25 = 2.69 (approximately)
However, none of the options given in the question have 2.69 as the radius. There may be a miscalculation in the completion of the square or the provided options could be incorrect. For a precise computation, we would reevaluate to ascertain the center (1, 1.5) and the exact radius, but it appears to not match the provided choices.
Since the correct values do not match the proposed choices, I cannot confidently select one of them as the correct answer. They all could be incorrect based on the calculation above.