Equations of hyperbolas 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 (±1, 0) that passes through (, 8)
In this problem we have to find an equation of the hyperbola with center at (0,0) with vertices ( 1 , 0) and passing through the point (,8).
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