Graphing hyperbolas Sketch the graph of the following hyperbolas. Specify the coordinates of the vertices and foci and find the equations of the asymptotes. Use a graphing utility to check your work.
10x2 − 7y2 = 140
In this problem we have to draw the graph of a hyperbola 10, and we have to label the vertices foci and the equation of asymptotes.
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
Step 2 :
- = 1.
By , using the above note .Here a = , b =
Therefore , vertices are ; ( a , 0) = ( , 0).
Eccentricity = = =
That is , e = = 1.55839 > 1.
Therefore , foci is ( ( ae , 0) = ( ( , 0) = (,0).
Equations of the asymptotes are ; y = x , and y = x.
Therefore , equations of the asymptotes are ; y = x and y = -x
y = x and y= - x