SOLUTION: For the hyperbola, find the equations of the asymptotes. x^2 - 4y^2 - 6x - 8y - 11 = 0 -------- After working the equation into standard form and having found the cent

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: For the hyperbola, find the equations of the asymptotes. x^2 - 4y^2 - 6x - 8y - 11 = 0 -------- After working the equation into standard form and having found the cent      Log On


   



Question 1204704: For the hyperbola, find the equations of the asymptotes.
x^2 - 4y^2 - 6x - 8y - 11 = 0
--------
After working the equation into standard form and having found the center and vertices, I wrote the equation of the asymptotes as
y = k +- b/a(x-h) => y = -1 +- 2/4(x-3)
But the answer I was provided was
x - 2y - 5 = 0
x + 2y - 1 = 0
What is this form?

Found 2 solutions by mananth, MathLover1:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify
y = -1 + 2/4(x-3)
y = -1 + 1/2(x-3)
multiply equation by 2
2y=-2+x-3
2y=x-5
2y-x+5=0
x-2y-5=0
y = -1 - 2/4(x-3)
2y=-2-x+3
2y= -x+1
x+2y-1=0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

that is general form form
The general form ax+%2Bby+%2Bc=0 is one of the many different forms you can write linear functions in.
so, y=-x%2F2%2B1%2F2 in general form is
y=+x%2F2-5%2F2..multiply by 2
2y=+x-5
0=+x-2y-5 switch sides
x-2y-5=0

and

y=-x%2F2%2B1%2F2...multiply by 2
2y=-x%2B1
x%2B2y-1=0