Use the discriminant to classify the graph. $x ^ { 2 } - 10 x y - 8 y ^ { 2 } - 18 = 0$
A)The graph is a parabola.
B)The graph is a hyperbola.
C)The graph is a ellipse.
D)The graph is a cone.
E)The graph is a circle.

Question

Use the discriminant to classify the graph.  $x ^ { 2 } - 10 x y - 8 y ^ { 2 } - 18 = 0$ 
A)The graph is a parabola.
B)The graph is a hyperbola.
C)The graph is a ellipse.
D)The graph is a cone.
E)The graph is a circle.

Quizplus · Accepted Answer

The given equation is of the form $Ax^2 + Bxy + Cy^2 + D = 0$, where $A = 1$, $B = -10$, and $C = -8$. The discriminant for such an equation is $B^2 - 4AC$. Substituting the values, we get $(-10)^2 - 4(1)(-8) = 100 + 32 = 132$, which is positive. A positive discriminant indicates that the graph is a hyperbola.

Use the Discriminant to Classify the Graph x2−10xy−8y2−18=0x ^ { 2 } - 10 x y - 8 y ^ { 2 } - 18 = 0x2−10xy−8y2−18=0

Use the Discriminant to Classify the Graph $x ^ { 2 } - 10 x y - 8 y ^ { 2 } - 18 = 0$