Solution Found!
Equations of hyperbolas Find an equation of the following
Chapter 9, Problem 45E(choose chapter or problem)
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 \((\pm6,\ 0)\)
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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