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Math Help - analytic geometry ( hyperbola)

  1. #1
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    analytic geometry ( hyperbola)

    find the equation of the path of a point that moves so that its distance from (5,0) is 5/4 of its distance from x=16/5
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  2. #2
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    Quote Originally Posted by ampong09 View Post
    find the equation of the path of a point that moves so that its distance from (5,0) is 5/4 of its distance from x=16/5

    A generic point (x,y)\in\mathbb{R}^2 fulfils the conditions iff \displaystyle{(x-5)^2+y^2=\frac{25}{16}\left(x-\frac{16}{5}\right)^2.

    That is a canonical hyperbola with x-axis equal to 4 and y-axis equal to ...

    Tonio
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  3. #3
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    can i have it in the standard form ? x^2/a^2 - y^2/b^2 = 1 ?
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    Quote Originally Posted by ampong09 View Post
    can i have it in the standard form ? x^2/a^2 - y^2/b^2 = 1 ?

    Of course you can: just re-arrange algebraically the equation I gave you.

    Tonio
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  5. #5
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    does this mean something ? http://www.mathhelpforum.com/math-he...5a4348339b.png it's my first time to use this in an equation. thanks for the answer
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    Quote Originally Posted by ampong09 View Post
    does this mean something ? http://www.mathhelpforum.com/math-he...5a4348339b.png it's my first time to use this in an equation. thanks for the answer

    That is what we use to symbolize a point in the plane \mathbb{R}^2... What is your level of mathematics?

    If you're doing analytic geometry you should understand the above, even if the symbology isn't known to you.

    Tonio
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