SOLUTION: A hyperbola has a vertical transverse axis of length 14 and asymptotes of y=9/8x + 1 and y= -9/8x - 9. Find the center of the hyperbola, its focal length, and its eccentricity.

Question 1039199: A hyperbola has a vertical transverse axis of length 14 and asymptotes of
y=9/8x + 1 and y= -9/8x - 9. Find the center of the hyperbola, its focal length, and its eccentricity.
Can you please show me the work to get the center mainly?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The center is the intersection of the asymptotes.
That is the point that is a solution to .
You can solve that system of equations by substitution.
For example, you could start by substituting the expression for in .
--> --> --> --> --> ,
and then, you could substitute the value found for one variable into one of the equations, to find the value of the other variable:
--> --> --> -->

The asymptotes slopes give you the ratio of conjugate to transverse axes.
The transverse axis is the segment joining the vertices of the hyperbola.
If the length is , the distance from the center to each vertex must be
.
From there you can find , , and the eccentricity: .

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