Which equation represents the circle with center at (0, 0) and radius 3?

Which equation represents the circle with center at (0, 0) and radius 3?

• A. x^2 + y^2 = 9
• B. x^2 + y^2 = 16
• C. (x-1)^2+(y-1)^2=9
• D. x^2 + (y-3)^2 = 9

Answer: (A)

For a circle, the standard form is (x − h)^2 + (y − k)^2 = r^2, where (h, k) is the center and r is the radius. If the center is at the origin, that becomes x^2 + y^2 = r^2. With radius 3, r^2 = 9, so the equation is x^2 + y^2 = 9. This matches the option that has center (0, 0) and radius 3. The other options describe circles with different centers or radii: x^2 + y^2 = 16 has radius 4; (x−1)^2 + (y−1)^2 = 9 centers at (1,1) with radius 3; x^2 + (y−3)^2 = 9 centers at (0,3) with radius 3.

For a circle, the standard form is (x − h)^2 + (y − k)^2 = r^2, where (h, k) is the center and r is the radius. If the center is at the origin, that becomes x^2 + y^2 = r^2. With radius 3, r^2 = 9, so the equation is x^2 + y^2 = 9. This matches the option that has center (0, 0) and radius 3. The other options describe circles with different centers or radii: x^2 + y^2 = 16 has radius 4; (x−1)^2 + (y−1)^2 = 9 centers at (1,1) with radius 3; x^2 + (y−3)^2 = 9 centers at (0,3) with radius 3.