Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.
-$$4 x ^ { 2 } - 2 y ^ { 2 } + 2 x + 8 y + 2 = 0$$
A) Parabola
B) Ellipse
C) Hyperbola

Question

Quizplus · Accepted Answer

The discriminant for a conic section given by the general equation $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is $B^2 - 4AC$. For the given equation, $A = 4$, $B = 0$, and $C = -2$, so the discriminant is $0^2 - 4(4)(-2) = 32$, which is positive, indicating that the conic section is a hyperbola.

Use the Discriminant to Decide Whether the Equation Represents a Parabola