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 a rotation of axes to eliminate the xy-term. (c) Sketch the graph.
Whether the graph of the equation is a parabola, an ellipse, or a hyperbola by the use of discriminant.
The equation is .
The graph of the general equation is either a conic or a degenerate conic. In the non degenerate cases, the graph is
1. If , then the graph is a parabola.
2. If , then the graph is an ellipse.
3. If , then the graph is a hyperbola.
Here, the is the discriminant.
The equation is
On comparing the general equation,
The equation without -term by the use of rotation of axes.
The graph of the equation .
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