Question 433652
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 to do!

The asymptotes of a hyperbola always intersect at the center.  So
all we need do is solve ths sayatem of equations

{{{system(y=expr(5/6)x+3,y=expr(-5/6)x+8)}}}

Add the two equations term by term and we get:

{{{2y = 11}}}

{{{y = 11/2}}}

Substituting in 

{{{y=expr(5/6)x+3}}}

{{{11/2=expr(5/6)+3}}}

Multiplying through by 6

{{{33=5x+18}}}

{{{15=5x}}}

{{{3=x}}}

So the center is (3,{{{11/2}}})

It doesn't matter about the transverse axis being 12.

Edwin</pre>