47-58 ■ Graphing Shifted Conics Complete the square to deter-mine whether the graph of the equation is an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyper-bola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation. If the equation has no graph, explain why.
The graph of the equation and its characteristics.
The given equation is,
The basic equation of the ellipse is,
The center of hyperbola is given by,
The focal length is given by,
The equation of asymptotes is given by,
Coordinates of vertex is given by,
Consider the given equation,
Now complete the square as shown below,
Compare the above equation with
This is the hyperbola with center .
Find the focal length of the ellipse,
Substitute for , and for in focal length formula
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