What is the equation of a circle with center at (2, -3) and radius 4? (2022)

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Question: What is the equation of a circle with center at (2, -3) and radius 4? (2022)

Options:

Correct Answer: (x-2)² + (y+3)² = 16

Exam Year: 2022

Solution:

The standard form of a circle\'s equation is (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=4. Thus, (x-2)² + (y+3)² = 16.

What is the equation of a circle with center at (2, -3) and radius 4? (2022)

What is the equation of a circle with center at (2, -3) and radius 4? (2022)

Step 1: Identify the center of the circle. The center is given as (2, -3). Here, h = 2 and k = -3.
Step 2: Identify the radius of the circle. The radius is given as 4.
Step 3: Recall the standard form of a circle's equation, 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-2)² + (y-(-3))² = 4².
Step 5: Simplify the equation. Since y-(-3) is the same as y+3, we have (x-2)² + (y+3)² = 16.
Step 6: Write the final equation of the circle: (x-2)² + (y+3)² = 16.

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