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Math Help - Hyperbolas.

  1. #1
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    Hyperbolas.

    I know how to write the equation of a hyperbola with its two branches (i.e. x^2/a^2-y^2/b^2=1 or vice versa), but can you write the equation of just one branch of the hyperbola? Would it just be the equation of a parabola?

    I know you could restrict the domain for those with horizontal transverse axes, but what about for vertical or in general?
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    Re: Hyperbolas.

    Your hyperbola equation is centred at (0,0) so you can restrict the domain as x>0 or x<0.
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    Re: Hyperbolas.

    Thanks, I understand that, but what if the transverse axis is vertical and I only want the top branch?
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    Re: Hyperbolas.

    O.k, you require a hyperbola that opens up top and bottom, which is \frac{y^2}{a^2}-\frac{x^2}{b^2}=1 which is also centred at the origin, you can restrict y>0
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    Re: Hyperbolas.

    And, in fact, for y> 0, you can solve for y: y= a\sqrt{1- \frac{x^2}{b^2}}.
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