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Math Help - What is this an equation of?

  1. #1
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    What is this an equation of?

    What does y^2-x^2=16 represent?

    I know it's a hyperbola, but I read that:

    if B2 − 4AC > 0, the equation represents a hyperbola;
    if we also have A + C = 0, the equation represents a rectangular hyperbola.

    Here A+C=0, but is this actually rectangular??? I thought it would just be a normal hyperbola....aren't rectangulars of the form xy=k
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  2. #2
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    Re: What is this an equation of?

    Quote Originally Posted by twittytwitter View Post
    What does y^2-x^2=16 represent?

    I know it's a hyperbola, but I read that:

    if B2 − 4AC > 0, the equation represents a hyperbola;
    if we also have A + C = 0, the equation represents a rectangular hyperbola.

    Here A+C=0, but is this actually rectangular??? I thought it would just be a normal hyperbola....aren't rectangulars of the form xy=k
    If you write this in standard form, you will have \displaystyle \begin{align*} \left(\frac{y}{4}\right)^2 - \left(\frac{x}{4}\right)^2 = 1 \end{align*}, so the asymptotes are \displaystyle \begin{align*} y = \pm \frac{4}{4}x = \pm x \end{align*}.

    Their gradients are \displaystyle \begin{align*} 1, -1 \end{align*}, which multiply to give \displaystyle \begin{align*} -1 \end{align*}. Therefore the gradients are perpendicular, so yes, it's a rectangular hyperbola
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  3. #3
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    Re: What is this an equation of?

    ok, thanks! I think I got it!
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