How do you find the center of the hyperbola, its focal length, and its eccentricity if a hyperbola has a vertical transverse axis of length 8 and asymptotes of #y=7/2x-3# and #y=-7/2x-1#?
The answers are:
Since this hyperbola has a vertical transverse axis (the "
First of all let's find the center that is at a point that is on the two asymptotes. So let's solve the system:
We can make a subtraction:
Since the asymptotes have slope:
and the vertical axis is
The equation of the hyperbola is:
The focal axis is named
The eccentricity is, in this case, is: