Q57 - Circle and circumference

The correct answer is D) It passes through the origin.

Quick check: substitute (0, 0): 0 + 0 + 0 + 0 = 0 ✓. Since the equation has no constant term, the origin always satisfies it.

For x² + y² + ax + by + c = 0, the centre is (−a/2, −b/2) and r² = (a/2)² + (b/2)² − c:

• Centre: (−5/2, −2)

• r² = 25/4 + 4 − 0 = 41/4, so r = √41/2 ≈ 3.2

A) Incorrect: The radius is √41/2, not zero.

B) Incorrect: A centre on the x-axis needs y = 0, but here it is −2.

C) Incorrect: A centre on the y-axis needs x = 0, but here it is −5/2.

D) Correct: No constant term, so (0, 0) lies on the circle.

E) Incorrect: A centre at the origin would require no x and y terms (a = b = 0).