Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.
-$$5 x ^ { 2 } - 7 x y - 2 y ^ { 2 } + 14 = 0$$
A) Ellipse
B) Parabola
C) Hyperbola

Question

Quizplus · Accepted Answer

The discriminant for a conic section given by $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is $B^2 - 4AC$. For this equation, $A = 5$, $B = -7$, and $C = -2$, so the discriminant is $(-7)^2 - 4(5)(-2) = 49 + 40 = 89$. Since the discriminant is positive, the equation represents a hyperbola.

Use the Discriminant to Decide Whether the Equation Represents a Parabola