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Math Help - Graph the equation of the translated graph in general form?

  1. #1
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    Graph the equation of the translated graph in general form?

    9x - 25y = 225 for T subscript(0, -5)

    This is what I did:

    9x - 25(y + 5) = 225
    9x - 25y - 250y - 850 = 0

    So to graph it I have to rewrite the general form equation in quadratic form, ay + by + c = 0, and then solve for y with the quadratic formula:

    (-25)y + (-250)y + (9x - 850) = 0

    y = {250√[(-250) - 4(-25)(9x - 850)]} / 2(-25)

    But when I try to graph it on a calculator it doesn't work. Help please!
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  2. #2
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    Re: Graph the equation of the translated graph in general form?

    Quote Originally Posted by explodingtoenails View Post
    9x - 25y = 225 for T subscript(0, -5)

    This is what I did:

    9x - 25(y + 5) = 225
    How did you get that?

    Are you aiming for a hyperbola \displaystyle \frac{x^2}{5^2}-\frac{y^2}{3^2}= 1 ?
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  3. #3
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    Re: Graph the equation of the translated graph in general form?

    The + 5 came from the ordered pair (0, -5) which was the translation I had to give respect to.

    And yes it is a hyperbola but the problem wanted it in general form, Ax + Bxy + Cy + Dx + Ey + F = 0.
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  4. #4
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    Re: Graph the equation of the translated graph in general form?

    Is the calculator window set correctly?
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  5. #5
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    Re: Graph the equation of the translated graph in general form?

    I guess not, but I have no idea what settings I should give to the window.
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  6. #6
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    Re: Graph the equation of the translated graph in general form?

    9x^2 - 25y^2 = 225 this hyperbola is centered at the origin.

    T_{(0,-5)} translates the hyperbola down 5 units ...

    9x^2 - 25(y+5)^2 = 225

    translated hyperbola
    Attached Thumbnails Attached Thumbnails Graph the equation of the translated graph in general form?-hyperbolatrans.jpg  
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  7. #7
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    Re: Graph the equation of the translated graph in general form?

    I'm very aware that I could have done that; the issue was that the book wanted the equation in GENERAL form before graphing (Ax + Bxy + Cy + Dx + Ey + F = 0).
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  8. #8
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    Re: Graph the equation of the translated graph in general form?

    Quote Originally Posted by explodingtoenails View Post
    I'm very aware that I could have done that; the issue was that the book wanted the equation in GENERAL form before graphing (Ax + Bxy + Cy + Dx + Ey + F = 0).
    fine, then expand the equation 9x^2 - 25(y+5)^2 = 225 after graphing ... note that the general form is not conducive to graphing.
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