In a coordinate plane, what is the equation of a circle with center at (3, -2) a

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Question: In a coordinate plane, what is the equation of a circle with center at (3, -2) and radius 4?

Options:

Correct Answer: (x - 3)² + (y + 2)² = 16

Solution:

The standard 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.

In a coordinate plane, what is the equation of a circle with center at (3, -2) and radius 4?

In a coordinate plane, what is the equation of a circle with center at (3, -2) and radius 4?

Step 1: Identify the center of the circle, which is given as (3, -2). Here, h = 3 and k = -2.
Step 2: Identify the radius of the circle, which is given as 4. So, r = 4.
Step 3: Use the standard form of the circle's equation: (x - h)² + (y - k)² = r².
Step 4: Substitute h and k into the equation: (x - 3)² + (y - (-2))² = r².
Step 5: Simplify the equation: (x - 3)² + (y + 2)² = r².
Step 6: Substitute r = 4 into the equation: (x - 3)² + (y + 2)² = 4².
Step 7: Calculate 4², which is 16: (x - 3)² + (y + 2)² = 16.

Circle Equation – Understanding the standard form of a circle's equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.