What is the equation of a circle with center at (1, 1) and radius 2?

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Question: What is the equation of a circle with center at (1, 1) and radius 2?

Options:

Correct Answer: (x - 1)² + (y - 1)² = 4

Solution:

The equation of a circle is (x - h)² + (y - k)² = r². Here, r = 2, so (x - 1)² + (y - 1)² = 2² = 4.

What is the equation of a circle with center at (1, 1) and radius 2?

What is the equation of a circle with center at (1, 1) and radius 2?

Step 1: Identify the center of the circle. The center is given as (1, 1). This means h = 1 and k = 1.
Step 2: Identify the radius of the circle. The radius is given as 2, so r = 2.
Step 3: Write down 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 - 1)² + (y - 1)² = 2².
Step 5: Calculate 2², which is 4. So the equation becomes (x - 1)² + (y - 1)² = 4.

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