To find :The standard equation of the hyperbola with given characteristics.
Answer to Problem 32RE
Explanation of Solution
Given information: Vertices of hyperbola are at (5,2) and (-5,2) and foci are at (6,2) and (-6,2)
Calculation:
The y-coordinates of the vertices and foci are the same, so the transverse axis is parallel to the x-axis. Therefore, the equation for hyperbola is of form
Where (h,k) is the center of hyperbola.
The center is halfway between the vertices (5,2) and (-5,2) .applying midpoint formula , we have
The vertices are 10 units apart, therefore 2a=10, that is a=5
Let 2c be the distance between the foci.
The foci are (6,2) and (-6,2), so 2c=12 and c=6.
Now,
Therefore, equation of hyperbola is
Chapter 10 Solutions
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