What is the radius of a circle with the equation (x - 2)² + (y + 3)² = 16?

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Question: What is the radius of a circle with the equation (x - 2)² + (y + 3)² = 16?

Options:

Correct Answer: 4

Solution:

The standard form of a circle is (x - h)² + (y - k)² = r². Here, r² = 16, so r = √16 = 4.

What is the radius of a circle with the equation (x - 2)² + (y + 3)² = 16?

What is the radius of a circle with the equation (x - 2)² + (y + 3)² = 16?

Step 1: Identify the equation of the circle, which is (x - 2)² + (y + 3)² = 16.
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: Compare the given equation to the standard form. Here, r² = 16.
Step 4: To find the radius (r), take the square root of r². So, r = √16.
Step 5: Calculate √16, which equals 4.
Step 6: Therefore, the radius of the circle is 4.

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