Equation of A Hyperbola

  • #1

Homework Statement


Find an equation of the hyperbola with it's center at the origin.

Foci:(8,0),(-8,0) Asymptotes: y=4x, y=-4x

Homework Equations


Equation for the asymptotes of a hyperbola with a horizontal transverse axis
[tex]y=k\pm\frac{b}{a}(x-h)[/tex]

Equation for a hyperbola centered at (0,0) and having a horizontal transverse axis in standard form

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

The Attempt at a Solution



Ok, so I need to find a and b to write the equation.

I can deduce from the information given that c=8 which is the distance from the center to a focus.

Therefore I can declare that [tex]a^2+b^2=64[/tex] and from looking at the asymptotes I can also declare that [tex]\frac{b}{a}=4[/tex]. I dont know how to solve a system of equations with division in it. Is there something I am missing?
 

Answers and Replies

  • #2
LCKurtz
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Put b = 4a from the second equation in the first equation and solve for a. Then solve for b.
 
  • #3
Put b = 4a from the second equation in the first equation and solve for a. Then solve for b.
Ahh.. Yes.

Thanks!
 

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