Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.
-$$x ^ { 2 } - 8 x y + 6 y ^ { 2 } - 13 = 0$$
A) Ellipse
B) Hyperbola
C) Parabola

Question

Quizplus · Accepted Answer

The discriminant for a conic section given by the general quadratic equation $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is $B^2 - 4AC$. For the given equation, $A = 1$, $B = -8$, and $C = 6$, so the discriminant is $(-8)^2 - 4(1)(6) = 64 - 24 = 40$. Since the discriminant is positive, the equation represents a hyperbola.

Use the Discriminant to Decide Whether the Equation Represents a Parabola