15-28 Graphing a Rotated Conic (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use 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 a discriminant.
The equation of the conic section is,
The graph of the equation
is either a conic or a degenerate conic. In the non-degenerate cases the graph is
• A parabola if .
• An ellipse if .
• A hyperbola if .
the quantity is called the discriminant of the equation.
Consider the equation.
Compare the equation with the equation of a conic section
Rotation of axes to eliminate the term.
The graph for the equation .
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