69–72 ■ Identifying a Conic An equation of a conic is given.
(a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the term. (c) Sketch the graph.
Whether the graph of the equation is a parabola, an ellipse, or a hyperbola using the discriminant.
The equation of the conic is .
The graph of the equation is
1. a parabola if ,
2. an ellipse if ,
3. a hyperbola if .
Here, the quantity is called the discriminant of the equation
The equation of the conic after eliminating the term using the rotation of axis.
The graph of the conic.
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started