Use the discriminant to classify the graph. $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$
A)The graph is a hyperbola.
B)The graph is a ellipse or circle.
C)The graph is a parabola.
D)The graph is a line.
E)The graph is a cone.

Question

Use the discriminant to classify the graph.  $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$ 
A)The graph is a hyperbola.
B)The graph is a ellipse or circle.
C)The graph is a parabola.
D)The graph is a line.
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, $A = 5$, $B = 10$, $C = 11$. The discriminant is $10^2 - 4(5)(11) = 100 - 220 = -120$, which is less than 0, indicating an ellipse or circle.

Use the Discriminant to Classify the Graph 5x2+10xy+11y2+9x−10y−72=05 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 05x2+10xy+11y2+9x−10y−72=0

Use the Discriminant to Classify the Graph $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$