Question #083fa
1 Answer
Center:
Focal length:
eccentricity:
Explanation:
Here is a reference for hyperbolas; the formulas and facts that I will say that we know can be found in this reference.
The center is at the intersection of the two asymptotes:
Substitute into the first equation:
Substitute into the standard Cartesian form for a hyperbola with a vertical transverse axis:
We know that the length of the vertical axis is
Given:
From the slopes of the asymptotes, we know that:
Substitute 8 for a:
The focal length, c, is:
We know that the eccentricity is