Use the discriminant to classify the graph. $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$
A)The graph is a hyperbola.
B)The graph is a line.
C)The graph is a ellipse or Circle.
D)The graph is a parabola.
E)The graph is a cone.

Question

Use the discriminant to classify the graph.  $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$ 
A)The graph is a hyperbola.
B)The graph is a line.
C)The graph is a ellipse or Circle.
D)The graph is a parabola.
E)The graph is a cone.

Quizplus · Accepted Answer

The discriminant for a conic section $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is $B^2 - 4AC$. Here, $A = 16$, $B = -5$, and $C = 10$. The discriminant is $(-5)^2 - 4(16)(10) = 25 - 640 = -615$. Since the discriminant is less than zero, the graph is an ellipse or a circle.

Use the Discriminant to Classify the Graph 16x2−5xy+10y2−44=016 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 016x2−5xy+10y2−44=0

Use the Discriminant to Classify the Graph $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$