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Math Help - Find vertex , focus and directrix of conic section

  1. #1
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    Find vertex , focus and directrix of conic section

    Find the vertex , focus and directrix of conic section
    <br />
4y^2 + 12x - 12y +39 = 0<br />
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  2. #2
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    Talking

    To learn the basic formulas and methods, try some online lessons.

    Once you have studied at least two lessons, please attempt the exercise. If you get stuck, you can then reply with a clear listing of your work and reasoning so far. Thank you!
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  3. #3
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    I am stuck

    Quote Originally Posted by stapel View Post
    To learn the basic formulas and methods, try some online lessons.

    Once you have studied at least two lessons, please attempt the exercise. If you get stuck, you can then reply with a clear listing of your work and reasoning so far. Thank you!

    4y^2 + 12x -12y + 39 = 0

    12x - 1 = -4 (y^2 - 3y -10)

    12x - 1 = -4 (y -5 ) (y + 2) .........I am stuck here !!!!
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  4. #4
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    Here maybe this will help you out a little...

    4y^{2}-12y = -12x-39
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    I tried this but still no go

    Quote Originally Posted by JSB1917 View Post
    Here maybe this will help you out a little...

    4y^{2}-12y = -12x-39

    4y^{2}-12y +8= -12x-39

    (4y-4)(y-2)= -12x-39.........stuck here
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  6. #6
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    Don't factor- complete the square!

    You want to arrive at x= a(y- b)^2+ c. When you have that you will know that the vertex is (c, b), that the focal distance is 1/(4a), and that the directrix is given by the line x= c-1/(4a).
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  7. #7
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    Quote Originally Posted by zorro View Post
    4y^{2}-12y +8= -12x-39

    (4y-4)(y-2)= -12x-39.........stuck here
    Not quite....

    4y^{2}-12y= -12x-39

    4(y^{2}-3y)= -12x-39

    4(y^{2}-3y+\frac{9}{4})= -12x-39+9

    4(y-\frac{3}{2})^{2}=-12x-30

    (y-\frac{3}{2})^{2}=-3x-\frac{15}{2}

    (y-\frac{3}{2})^{2}=-3(x+\frac{5}{2})
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  8. #8
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    \therefore y^2 = - 4ax

     vertex = ( \frac{-5}{2} , \frac{3}{2})

    4a = 3 => a = \frac{3}{4}

    focus = (-a,0) = (-\frac{3}{4},0)

    directrix x= \frac{3}{4}..........Is this correct????
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