Find asymptotes on a hyperbola graph?

**DHS1** · December 15th 2012, 09:37 PM

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^2-10y^2=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

**Prove It** · December 15th 2012, 09:59 PM

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?

**DHS1** · December 15th 2012, 11:46 PM

So it looks like this?

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