Use the discriminant to classify the graph. $x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0$
A)The graph is a parabola.
B)The graph is a hyperbola.
C)The graph is a line.
D)The graph is a circle.
E)The graph is a ellipse.

Question

Use the discriminant to classify the graph.​ $x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0$ ​
A)The graph is a parabola.
B)The graph is a hyperbola.
C)The graph is a line.
D)The graph is a circle.
E)The graph is a ellipse.

Quizplus · Accepted Answer

The discriminant for a conic section $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is $B^2 - 4AC$. Here, $A = 1$, $B = 6$, and $C = 9$. The discriminant is $6^2 - 4(1)(9) = 36 - 36 = 0$, indicating a parabola.

Use the Discriminant to Classify the Graph x2+6xy+9y2−5x−y−3=0x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0x2+6xy+9y2−5x−y−3=0

Use the Discriminant to Classify the Graph $x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0$