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Math Help - Parabola, Elipses, Hyperbola help?

  1. #1
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    Parabola, Elipses, Hyperbola help?

    Hey. I have a math quiz tomorrow, and am working on a worksheet with 20 problems. I'm not sure I understand these problems, so if possible can someone please possibily solve these samples? I was absent, and am totally loss.

    1. Find standard form for parabola:
    Foci(4,-1) directrix: y= 3

    2. Elipses:
    (x+4)^2/ 9 + (y-3)^2/ 36= 1.
    Find vertices, foci, length of major and minor axis.

    3. Hyperbolas:
    4x^2 - 6y^2 - 24y+ 8x - 12= 0
    State center, vericies, and foci.

    Basically, each of these 3 types are the kinds I'll be expected to know how to solve on the quiz tomorrow. I need samples done, so I can understand the processes. At the moment I'm clueless as to how to solve them. Any and all help will be appreciated!

    ~ Dracos
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  2. #2
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    Hello Dracos

    Welcome to Math Help Forum!
    Quote Originally Posted by Dracos View Post
    Hey. I have a math quiz tomorrow, and am working on a worksheet with 20 problems. I'm not sure I understand these problems, so if possible can someone please possibily solve these samples? I was absent, and am totally loss.

    1. Find standard form for parabola:
    Foci(4,-1) directrix: y= 3

    2. Elipses:
    (x+4)^2/ 9 + (y-3)^2/ 36= 1.
    Find vertices, foci, length of major and minor axis.

    3. Hyperbolas:
    4x^2 - 6y^2 - 24y+ 8x - 12= 0
    State center, vericies, and foci.

    Basically, each of these 3 types are the kinds I'll be expected to know how to solve on the quiz tomorrow. I need samples done, so I can understand the processes. At the moment I'm clueless as to how to solve them. Any and all help will be appreciated!

    ~ Dracos
    For help on the parabola, you could look here.

    For the ellipse, this is not bad.

    For the hyperbola, you need to complete the square:
    4(x^2+2x+1)-6(y^2+4y+4)+8=0
    before re-writing in its standard form:
    \frac{(y+2)^2}{\tfrac43}-\frac{(x+1)^2}{2}=1
    and then look here.

    Grandad
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