SOLUTION: I need help with this problem? The equation of a hyperbola is {{{4y^2 - x^2 + 8y - 6x - 41 = 0.}}} Write the equation of the hyperbola in standard form and find the coordinates of

Question 982534: I need help with this problem? The equation of a hyperbola is Write the equation of the hyperbola in standard form and find the coordinates of the center, the coordinates of the vertices, and the equation of the asymptotes. Then graph the hyperbola.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

....complete square

The standard form of an hyperbola with the transverse axis being vertical.

The center of the hyperbola is at the point ( ,) or (,)
and , so
semimajor axis length
semiminor axis length
The foci are units from the center of the hyperbola and is calculated from .
=>=>
The foci are therefore, ( , ) or ( , )
or (,) and (, ()
=>(,) and (, )
The vertices are a units from the center of the hyperbola, ( , ) and ( , )
or ( , ) and ( , )

asymptotes:

RELATED QUESTIONS
x^2+4x+4-4y^2+8y-8=0 Is this an equation for a hyperbola? How do I find the center,... (answered by Edwin McCravy)

Would you please help me with a problem I don't seem to understand how to do? I need help (answered by lwsshak3)

What is the center of this hyperbola:... (answered by lwsshak3)

I need some help solving a problem. The problem: Find the standard form of the... (answered by lwsshak3)

I cannot seem to find the correct standard equation, foci, and asymptotes of the... (answered by Edwin McCravy)

For the hyperbola, find the equations of the asymptotes. x^2 - 4y^2 - 6x - 8y -... (answered by mananth,MathLover1)

Find the standard equation of a hyperbola when you're given this equation : x^2 - 4y^2... (answered by robertb)

Write the equation in standard form. State whether the graph of the equation is a... (answered by lwsshak3)

i need some help with question.. the equation of the asymptotes of the hyperbola... (answered by jim_thompson5910)