What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?

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Question: What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?

Options:

Correct Answer: 4

Solution:

The radius is the square root of 16, which is 4.

What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?

What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?

Step 1: Identify the equation of the circle, which is (x - 1)² + (y + 4)² = 16.
Step 2: Recognize that the general 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.
Step 3: In our equation, the right side is 16, which represents r².
Step 4: To find the radius (r), take the square root of 16.
Step 5: Calculate the square root of 16, which is 4.
Step 6: Conclude that the radius of the circle is 4.

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