10
QuizMultiple Choice

The General Equation of Conic Sections — Quiz

Question 10 • Precalculus

Which equation represents a parabola?

Answer
A
negative 3 x plus 4 y squared minus 2 y plus 6 is equal to 0
B
x squared plus x minus 2 y squared minus 4 y plus 2 is equal to 0
C
4 x squared minus 2 x plus 3 y squared minus y plus 1 is equal to 0
D
2 x squared plus y squared minus 4 y plus 6 is equal to 0

Explanation

A parabola has a squared term for one variable but not the other. Choice C, −3x + 4y² − 2y + 6 = 0, has y² but no x²; rearranging gives x = (4/3)y² − (2/3)y + 2, which is a parabola. The other choices contain squared terms for both x and y.

AI-written and checked against the verified answer.