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Equations of hyperbolas Find an equation of the following
Chapter 9, Problem 45E(choose chapter or problem)
Questions & Answers
QUESTION:
Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work.
A hyperbola with vertices \((\pm4,\ 0)\) and foci \((\pm6,\ 0)\)
ANSWER:Solution 45E
Step 1:
In this problem we have to find an equation of the hyperbola with center at (0 ,0) with vertices ( 4 , 0) and foci ( 6 , 0).
Note; We know that a hyperbola with the center of its origin .For these hyperbolas , the standard form of the equation is  =1 for hyperbolas that extend right and left (or)  =1for hyperbolas that extend up and down.
Consider ,  =1 . In this case
Center is ;(0,0) , vertices are ;( a, 0) ,(a,0) , and foci is ( ae, 0) (ae,0).
Equations of the asymptotes are ; y = x , and y = x

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