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

Based on the shape of the graph, it can either be an ellipse or a circle. The discriminant for an ellipse or circle is ((B^2 - 4AC)/D) where A, B, and C are the coefficients of x^2, xy, and y^2 terms respectively and D is the denominator of the equation. In this case, the discriminant is positive, indicating that the graph is either 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 $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$