Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.
-$$x ^ { 2 } + 4 x y + 6 y ^ { 2 } - 2 x + 4 y = 0$$
A) Hyperbola
B) Parabola
C) Ellipse

Question

Quizplus · Accepted Answer

The given equation is a second-degree equation in two variables, x and y. To determine the type of conic section it represents (parabola, ellipse, or hyperbola), we look at the discriminant of the quadratic part, which is given by $B^2 - 4AC$, where $A$, $B$, and $C$ are the coefficients of $x^2$, $xy$, and $y^2$ respectively. In this case, $A = 1$, $B = 4$, and $C = 6$. Thus, the discriminant is $4^2 - 4(1)(6) = 16 - 24 = -8$. Since the discriminant is negative, the equation represents an ellipse.

Use the Discriminant to Decide Whether the Equation Represents a Parabola