Which of the following equations represents a circle with a center at (3, -2) an

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Question: Which of the following equations represents a circle with a center at (3, -2) and a radius of 5?

Options:

Correct Answer: (x - 3)² + (y + 2)² = 25

Solution:

The standard form of a circle\'s equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Which of the following equations represents a circle with a center at (3, -2) and a radius of 5?

Which of the following equations represents a circle with a center at (3, -2) and a radius of 5?

Step 1: Identify the center of the circle, which is given as (3, -2). Here, h = 3 and k = -2.
Step 2: Identify the radius of the circle, which is given as 5. So, r = 5.
Step 3: Use the standard form of a circle's equation: (x - h)² + (y - k)² = r².
Step 4: Substitute h and k into the equation: (x - 3)² + (y - (-2))² = r².
Step 5: Simplify the equation: (x - 3)² + (y + 2)² = r².
Step 6: Substitute r = 5 into the equation: (x - 3)² + (y + 2)² = 5².
Step 7: Calculate 5², which is 25: (x - 3)² + (y + 2)² = 25.

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