SOLUTION: A hyperbola has a vertical transverse axis of 12 and asymptotes of {{{y=expr(5/6)x+3}}} and {{{y=expr(-5/6)x+8}}} Find the center of the hyperbola Please help, I don't know what t

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A hyperbola has a vertical transverse axis of 12 and asymptotes of {{{y=expr(5/6)x+3}}} and {{{y=expr(-5/6)x+8}}} Find the center of the hyperbola Please help, I don't know what t      Log On


   

Question 433652: A hyperbola has a vertical transverse axis of 12 and asymptotes of y=expr%285%2F6%29x%2B3 and y=expr%28-5%2F6%29x%2B8 Find the center of the hyperbola
Please help, I don't know what to do!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A hyperbola has a vertical transverse axis of 12 and asymptotes of y=expr%285%2F6%29x%2B3 and y=expr%28-5%2F6%29x%2B8 Find the center of the hyperbola
Please help, I don't know what to do!
The asymptotes of a hyperbola always intersect at the center. So
all we need do is solve ths sayatem of equations
system%28y=expr%285%2F6%29x%2B3%2Cy=expr%28-5%2F6%29x%2B8%29
Add the two equations term by term and we get:
2y+=+11
y+=+11%2F2
Substituting in
y=expr%285%2F6%29x%2B3
11%2F2=expr%285%2F6%29%2B3
Multiplying through by 6
33=5x%2B18
15=5x
3=x
So the center is (3,11%2F2)
It doesn't matter about the transverse axis being 12.
Edwin