To Find: The equation of a conic from the given graph.
Answer to Problem 6T
The equation of a shifted conic is
Explanation of Solution
Definition used: 1
“The equation of the shifted hyperbola with center as
Definition used: 2
“The equation of asymptotes of the shifted hyperbola
Calculation:
From the given graph, it is observed that the graph is a hyperbola with horizontal axix as transverse axis and the vertices are
Let
Since the center of the hyperbola is the midpoint of the vertices, compute the midpoint.
Therefore, the center of the ellipse is
Compute the distance between the vertices.
By the above definition (1), compute the equation of the shifted ellipse.
Therefore, by definition (1), the equation of conic is
Since the equation
Simplify the terms further,
Substitute
Therefore, the equation of conic is
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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