What is the radius of a circle with the equation (x - 4)² + (y + 2)² = 36?

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Question: What is the radius of a circle with the equation (x - 4)² + (y + 2)² = 36?

Options:

Correct Answer: 6

Solution:

The standard form of a circle is (x - h)² + (y - k)² = r². Here, r² = 36, so r = √36 = 6.

What is the radius of a circle with the equation (x - 4)² + (y + 2)² = 36?

What is the radius of a circle with the equation (x - 4)² + (y + 2)² = 36?

Step 1: Identify the equation of the circle, which is (x - 4)² + (y + 2)² = 36.
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 36, which represents r².
Step 4: To find the radius (r), take the square root of r². So, r = √36.
Step 5: Calculate √36, which equals 6.
Step 6: Therefore, the radius of the circle is 6.

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