Use the discriminant to identify the graph of
$2 x^{2}+4 x y-2 y^{2}-3 x-y=8$
A) The graph is a circle.
B) The graph is a hyperbola.
C) The graph is an ellipse.
D) The graph is a parabola.

Question

Use the discriminant to identify the graph of 
$2 x^{2}+4 x y-2 y^{2}-3 x-y=8$
A) The graph is a circle.
B) The graph is a hyperbola.
C) The graph is an ellipse.
D) The graph is a parabola.

Quizplus · Accepted Answer

The given equation can be rewritten in the form of a quadratic equation in two variables, which is $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$. The discriminant of such an equation is given by $B^2 - 4AC$. Substituting the given values, we get $4^2 - 4(2)(-2) = 16 + 16 = 32$, which is positive. A positive discriminant indicates that the graph is a hyperbola.

Use the Discriminant to Identify the Graph Of 2x2+4xy−2y2−3x−y=82 x^{2}+4 x y-2 y^{2}-3 x-y=82x2+4xy−2y2−3x−y=8

Use the Discriminant to Identify the Graph Of $2 x^{2}+4 x y-2 y^{2}-3 x-y=8$