Equations of hyperbolas Find an equation of the following

Chapter 9, Problem 45E

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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 $$(\pm6,\ 0)$$

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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