Use the discriminant to classify the graph. $36 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 0$
A)The graph is a cone.
B)The graph is a circle.
C)The graph is a parabola.
D)The graph is a ellipse.
E)The graph is a hyperbola.

Question

Use the discriminant to classify the graph.  $36 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 0$ 
A)The graph is a cone.
B)The graph is a circle.
C)The graph is a parabola.
D)The graph is a ellipse.
E)The graph is a hyperbola.

Quizplus · Accepted Answer

The discriminant of a conic section $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is $B^2 - 4AC$. For the given equation, $A = 36$, $B = -144$, and $C = 1$. The discriminant is $(-144)^2 - 4(36)(1) = 20736 - 144 = 20592$, which is greater than zero, indicating a hyperbola.

Use the Discriminant to Classify the Graph 36x2−144xy+y2−10x+5y=036 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 036x2−144xy+y2−10x+5y=0

Use the Discriminant to Classify the Graph $36 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 0$