Results 1 to 3 of 3

Math Help - Find asymptotes on a hyperbola graph?

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    30

    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^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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293

    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?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2008
    Posts
    30

    Re: Find asymptotes on a hyperbola graph?

    So it looks like this?

    Find asymptotes on a hyperbola graph?-imag0578.jpg
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 27th 2012, 01:22 PM
  2. Replies: 4
    Last Post: November 27th 2012, 01:22 PM
  3. Replies: 2
    Last Post: September 3rd 2012, 11:32 AM
  4. Asymptotes of a hyperbola
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 17th 2009, 03:42 AM
  5. Asymptotes of a Hyperbola
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 31st 2009, 07:25 AM

Search Tags


/mathhelpforum @mathhelpforum