What is the equation of a circle with center at (3, -2) and radius 5? (2022)

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Question: What is the equation of a circle with center at (3, -2) and radius 5? (2022)

Options:

Correct Answer: (x-3)² + (y+2)² = 25

Exam Year: 2022

Solution:

The standard form of a circle\'s equation is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=5, so (x-3)² + (y+2)² = 25.

What is the equation of a circle with center at (3, -2) and radius 5? (2022)

What is the equation of a circle with center at (3, -2) and radius 5? (2022)

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: 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 means replacing h with 3, k with -2, and r with 5.
Step 5: The equation becomes (x-3)² + (y-(-2))² = 5².
Step 6: Simplify the equation. Since y-(-2) is the same as y+2, the equation is (x-3)² + (y+2)² = 25.

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