What is the equation of a circle centered at the origin with radius 5?

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Multiple Choice

What is the equation of a circle centered at the origin with radius 5?

Explanation:
A circle is all the points at a fixed distance from its center, so its equation in standard form is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius. If the center is at the origin, h = 0 and k = 0, giving x² + y² = r². With a radius of 5, r² = 25, so the equation is x² + y² = 25. The other forms correspond to centers at (5, 0) or (0, 5) or use a different radius, so they don’t describe a circle centered at the origin with radius 5.

A circle is all the points at a fixed distance from its center, so its equation in standard form is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius. If the center is at the origin, h = 0 and k = 0, giving x² + y² = r². With a radius of 5, r² = 25, so the equation is x² + y² = 25. The other forms correspond to centers at (5, 0) or (0, 5) or use a different radius, so they don’t describe a circle centered at the origin with radius 5.

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