What is the radius of a circle with the equation (x - 3)² + (y + 2)² = 25?

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Question: What is the radius of a circle with the equation (x - 3)² + (y + 2)² = 25?

Options:

Correct Answer: 5

Solution:

The standard form of a circle is (x - h)² + (y - k)² = r². Here, r² = 25, so r = √25 = 5.

What is the radius of a circle with the equation (x - 3)² + (y + 2)² = 25?

What is the radius of a circle with the equation (x - 3)² + (y + 2)² = 25?

Step 1: Identify the equation of the circle, which is (x - 3)² + (y + 2)² = 25.
Step 2: Recognize that the standard form of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Step 3: In the given equation, the right side is 25, which represents r².
Step 4: To find the radius (r), take the square root of r². So, r = √25.
Step 5: Calculate √25, which equals 5.
Step 6: Therefore, the radius of the circle is 5.

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