Find asymptotes on a hyperbola graph?

• December 15th 2012, 10:37 PM
DHS1
Find asymptotes on a hyperbola graph?
Sketch the graph of the given equation of a hyperbola. Be sure to label the center, verticies, foci, transverse and conjugate axes, and asymptotes. x^2-10y^2=40

I have the graph of the hyperbola here: x&#94;2-10y&#94;2&#61;40 - Wolfram|Alpha

How do I get the asymptotes? I have an equation that asymptotes: y=+- (a/b)x. I know a = 2*(sqrt(10) and b = 2. But how do I label them on the graph? Am I doing something wrong?

Thanks
• December 15th 2012, 10:59 PM
Prove It
Re: Find asymptotes on a hyperbola graph?
If you can write your equation in the form \displaystyle \begin{align*} \frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1 \end{align*} then it is centred at \displaystyle \begin{align*} (h, k) \end{align*} and has asymptotes at \displaystyle \begin{align*} y = k \pm \frac{b}{a} \left( x - h \right) \end{align*}. So in your case:

\displaystyle \begin{align*} x^2 - 10y^2 &= 40 \\ \frac{x^2 - 10y^2}{40} &= 1 \\ \frac{x^2}{40} - \frac{y^2}{4} &= 1 \\ \frac{x^2}{\left( 2\sqrt{10} \right)^2} - \frac{y^2}{2^2} &= 1 \end{align*}

Can you read off the centre and asymptotes now?
• December 16th 2012, 12:46 AM
DHS1
Re: Find asymptotes on a hyperbola graph?
So it looks like this?

Attachment 26254