中等MATH-GEOM-012
The equation x^2 + y^2 + Dx + Ey + F = 0 represents a circle of positive radius when
A. D^2 + E^2 − 4F < 0
B. D^2 + E^2 − 4F = 0
C. D^2 + E^2 − 4F > 0✓ 答案
D. F > 0
解說
The radius is (1/2)√(D^2 + E^2 − 4F). This is positive exactly when D^2 + E^2 − 4F > 0. Equality gives a single point, and a negative value gives no real point.