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Math Help - math help please

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    7

    math help please

    Hello, i need help trying to solve these problems, dont understand how to arrive to answers... thak you very much in advance..


    Solve-
    1)4x^2+9y^2-16x+18y-11=0

    2) y^2= -20x vertex foci

    3) Sin^2x-sinx= 0
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  2. #2
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    honolulu
    Posts
    580

    complete the quare

    4x^2+9y^2-16x+18y-11=0

    this is an ellipse and you will need to complete the square to solve it

    the Ellipse Equation is
    <br />
\frac{\left(x - h\right)^2}{a^2} + \frac{\left(y - k\right)^2}{b^2} = 1

    rewrite

    4x^2-16x  +9y^2+18y   =  11

    factor out

    4\left(x^2-4x      \right)+ 9\left(y^2+2y    \right) = 11

    now add in so squares can be construted

    4\left(x^2-4x + 4 \right)+ 9\left(y^2+2y + 1 \right) = 11+16 +9  = 36

    factor the squares

    4\left(x^2-2\right)^2+ 9\left(y^2+1\right)^2 = 36

    divide thru with 36 and simplify

    \frac{\left(x^2-2\right)^2}{3^2}+ \frac{\left(y^2+1\right)^2}{2^2} = 1
    foci:  \left(h \pm c,k\right)
    vertices:  \left(h \pm a,k\right)
    axis  \left(h,k \pm b\right)
    Last edited by bigwave; December 16th 2009 at 08:10 PM. Reason: more info
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  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    62
    y^2 = -20x vertex foci

    Use 4p for this.

    \sin^2{x} - \sin{x}= 0

    Treat this like an algebra problem....

    \sin{x}(\sin{x} - 1) = 0

    Then think of values where

    \sin{x} = 0 and \sin{x} = 1
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