When does the equation x² + y² + z² + Ax + By + Cz + D = 0 represent a sphere? A) if and only if A² + B² + C² + D 0 B) if and only if A² + B² - C² D C) if and only if A² - B² + C² 0 D) if and only if A² + B² + C² 4D E) if and only if A = 0, B = 0, C = 0, and D

Question

When does the equation x² + y² + z² + Ax + By + Cz + D = 0 represent a sphere? A) if and only if A² + B² + C² + D > 0 B) if and only if A² + B² - C² > D C) if and only if A² - B² + C² > 0 D) if and only if A² + B² + C² > 4D E) if and only if A = 0, B = 0, C = 0, and D < 0

Quizplus · Accepted Answer

The equation represents a sphere if the coefficients of x, y, and z can be completed to form a perfect square, which requires A² + B² + C² > 4D to ensure a positive radius squared.

When Does the Equation X2 + Y2 + Z2

When Does the Equation X² + Y² + Z²