Use the discriminant to determine whether the graph of the equation is a parabola, ellipse, or a hyperbola. $13 x ^ { 2 } - 10 x y + 13 y ^ { 2 } - 72 = 0$
A)parabola
B)ellipse
C)hyperbola

Question

Quizplus · Accepted Answer

The discriminant for a conic section given by $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is $B^2 - 4AC$. For this equation, $A = 13$, $B = -10$, and $C = 13$, so the discriminant is $(-10)^2 - 4(13)(13) = 100 - 676 = -576$. Since the discriminant is negative, the graph is an ellipse.

Use the Discriminant to Determine Whether the Graph of the Equation