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Math Help - Rectangular Hyperbola

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    Rectangular Hyperbola

    I don't understand how to do part (c). Can someone help? Also, if possible can someone draw it so I can see how it is pictured. Thanks in advance.
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  2. #2
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    Quote Originally Posted by Air View Post
    I don't understand how to do part (c). Can someone help? Also, if possible can someone draw it so I can see how it is pictured. Thanks in advance.
    (c) Obviously M has coordinates \left(\frac{cp + 2pc}{2}, \, \frac{\frac{c}{p} + \frac{c}{2p}}{2}\right), that is, \left(\frac{3cp}{2}, \, \frac{3c}{4p}\right).

    So the equation of the locus has parametric equations:

    x = \frac{3cp}{2} .... (1)

    y = \frac{3c}{4p} .... (2)

    and p \in R \setminus \{0\}.

    From (1): p = \frac{2x}{3c}.

    From (2): p = \frac{3c}{4y}.

    Therefore \frac{2x}{3c} = \frac{3c}{4y} \Rightarrow xy = \frac{9 c^2}{8} ....
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