What is the equation of the circle with center (3, -2) and radius 5?

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Question: What is the equation of the circle with center (3, -2) and radius 5?

Options:

Correct Answer: (x-3)² + (y+2)² = 25

Solution:

Equation of circle: (x-h)² + (y-k)² = r² => (x-3)² + (y+2)² = 5² = 25.

What is the equation of the circle with center (3, -2) and radius 5?

What is the equation of the circle with center (3, -2) and radius 5?

Step 1: Identify the center of the circle. The center is given as (3, -2). Here, h = 3 and k = -2.
Step 2: Identify the radius of the circle. The radius is given as 5.
Step 3: Write the general equation of a circle, which is (x - h)² + (y - k)² = r².
Step 4: Substitute the values of h, k, and r into the equation. This gives us (x - 3)² + (y - (-2))² = 5².
Step 5: Simplify the equation. Since y - (-2) is the same as y + 2, we have (x - 3)² + (y + 2)² = 25.

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