# Find an equation

• Jan 18th 2013, 11:07 AM
Itel
Find an equation
Can someone help walk me through this problem? I'd really appreciate your help.

Find an equation in standard form for the hyperbola with vertices at (0, -10) and asymptotes at y= +-(5/4)x
• Jan 18th 2013, 11:39 AM
MarkFL
Re: Find an equation
If the transverse axis is on the y-axis, then the form of the hyperbola is:

$\displaystyle \frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ where $\displaystyle 0<a,b$.

Since the vertices are (presumably) at $\displaystyle (0,\pm10)$, then what is the value of a?

The asymptotes will be at $\displaystyle y=\pm\frac{a}{b}x$, so from the given asymptotes, we know:

$\displaystyle \frac{a}{b}=\frac{5}{4}$

$\displaystyle b=\frac{4}{5}a$

Use the value you found for a to find b.

and so what is the equation of the hyperbola?
• Jan 18th 2013, 12:29 PM
Itel
Re: Find an equation
Would a be -10?

Which would make b 8?
• Jan 18th 2013, 12:35 PM
MarkFL
Re: Find an equation
a and b are both positive, so $\displaystyle a=10$ and yes, then $\displaystyle b=8$.
• Jan 18th 2013, 12:41 PM
Itel
Re: Find an equation
So the equation would just be

y^2/100 - x^2/64 = 1?
• Jan 18th 2013, 12:47 PM
MarkFL
Re: Find an equation
Yes, although the standard form is:

$\displaystyle \frac{y^2}{10^2}-\frac{x^2}{8^2}=1$
• Jan 18th 2013, 01:02 PM
Itel
Re: Find an equation
Thank you so much for your help. I really appreciate it.