To find: The standard form of the equation of hyperbola with the given characteristics.
Answer to Problem 46E
The standard form of the equation of hyperbola is
Explanation of Solution
Given information:
The characteristics are vertices:
Calculation:
The center is the midpoint of the vertices.
The distance between one of the vertices and the center is
The vertices lie on a vertical line. So, the hyperbola has a vertical transverse axis. Use the formula for the asymptotes of a hyperbola with a vertical transverse axis.
Substitute the center and a into the formula as shown below.
Solve for b by comparing the equation to the two given asymptotes.
Substitute 3 for
Therefore, the standard form of the equation of hyperbola is
Chapter 9 Solutions
Precalculus with Limits: A Graphing Approach
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