If the center of a circle is at (2, 3) and the radius is 5, what is the equation

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Question: If the center of a circle is at (2, 3) and the radius is 5, what is the equation of the circle?

Options:

Correct Answer: (x - 2)² + (y - 3)² = 25

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.

If the center of a circle is at (2, 3) and the radius is 5, what is the equation of the circle?

If the center of a circle is at (2, 3) and the radius is 5, what is the equation of the circle?

Step 1: Identify the center of the circle, which is given as (2, 3). Here, h = 2 and k = 3.
Step 2: Identify the radius of the circle, which is given as 5. So, r = 5.
Step 3: Write 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 - 2)² + (y - 3)² = r².
Step 5: Substitute r into the equation: (x - 2)² + (y - 3)² = 5².
Step 6: Calculate 5², which is 25. So, the equation becomes (x - 2)² + (y - 3)² = 25.

Circle Equation – Understanding the standard form of a circle's equation, which is derived from its center and radius.