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Math Help - Graph the ellipse and graph the hyperbola

  1. #1
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    Unhappy Graph the ellipse and graph the hyperbola

    Please help me solve the following ellipse problem:

    Graph the ellipse. 16x^2+4y^2=48

    what is the center?
    Where are the vertices?
    Where are the co-vertices?
    Where are the foci?




    Graph the hyperbola. 16y^2-4x^2=64
    What is the center?
    What are the vertices?
    Where are the co-vertices?
    Where are the foci?
    What are the asymptotes?
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  2. #2
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    Quote Originally Posted by smartcp View Post
    Graph the ellipse. 16x^2+4y^2=48

    what is the center?
    Where are the vertices?
    Where are the co-vertices?
    Where are the foci?
    Most folks resort to a Standard Form, usually this one

    \frac{x^{2}}{3} + \frac{y^{2}}{12} = 1

    Using standard notation:

    This makes a = \sqrt{3}, and b = 2\sqrt{3}

    Find 'c' and you nearly are done.

    Note: If you REALLY cannot find the center of this one, you MUST go back and reread a section or two. You missed something very important.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by smartcp View Post
    Please help me solve the following ellipse problem:

    Graph the ellipse. 16x^2+4y^2=48

    what is the center?
    Where are the vertices?
    Where are the co-vertices?
    Where are the foci?




    Graph the hyperbola. 16y^2-4x^2=64
    What is the center?
    What are the vertices?
    Where are the co-vertices?
    Where are the foci?
    What are the asymptotes?
    Graph of Ellipse:


    I'll let you figure out the rest.

    Graph of Hyperbola:



    Try to figure out the rest.
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  4. #4
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    Quote Originally Posted by smartcp View Post
    Please help me solve the following ellipse problem:

    Graph the ellipse. 16x^2+4y^2=48

    what is the center?
    Where are the vertices?
    Where are the co-vertices?
    Where are the foci?




    Graph the hyperbola. 16y^2-4x^2=64
    What is the center?
    What are the vertices?
    Where are the co-vertices?
    Where are the foci?
    What are the asymptotes?
    1.)
    16x^2+4y^2=48
    \frac{x^2}{3}  + \frac{y^2}{12} = 1


    2.)
    16y^2-4x^2=64
    \frac{y^2}{4}  - \frac{x^2}{16}=1


    Standard form: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
    Vertices: (\pm a, 0)
    Co-vertices: (0, \pm b)
    Eccentricity: e<1, \ \ b^2 = a^2(1-e^2)
    Foci: (\pm ae, 0)
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