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Thread: Analytic Geometry: Ellipse [2]

  1. #1
    Member looi76's Avatar
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    Analytic Geometry: Ellipse [2]

    Question:
    Find the coordinates of the foci, the end points of the major axes and minor axis, the length of latus rectum and the end points of latus rectum.

    $\displaystyle \frac{(x-3)^2}{16} + \frac{(y-2)^2}{9} = 1$

    Attempt:

    Center: $\displaystyle (3,2)$ $\displaystyle a=4$, $\displaystyle b=3$ , $\displaystyle c=\sqrt{16-9} = \sqrt{7}$

    Foci:$\displaystyle (3-\sqrt{7},2)$ and $\displaystyle (3+\sqrt{7},2)$

    End points of major axis: $\displaystyle (-1,2)$ and $\displaystyle (7,2)$

    End points of minor axis: $\displaystyle (3,-1)$ and $\displaystyle (3,5)$

    Length of latus rectum: $\displaystyle 2\frac{b^2}{a} = 2\frac{(3)^2}{4} = \frac{9}{2}$


    How can I find out the end points of latus rectum? and are my answers right tell now?
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  2. #2
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    Ellipse

    Hello looi76
    Quote Originally Posted by looi76 View Post
    Question:
    Find the coordinates of the foci, the end points of the major axes and minor axis, the length of latus rectum and the end points of latus rectum.

    $\displaystyle \frac{(x-3)^2}{16} + \frac{(y-2)^2}{9} = 1$

    Attempt:

    Center: $\displaystyle (3,2)$ $\displaystyle a=4$, $\displaystyle b=3$ , $\displaystyle c=\sqrt{16-9} = \sqrt{7}$

    Foci:$\displaystyle (3-\sqrt{7},2)$ and $\displaystyle (3+\sqrt{7},2)$

    End points of major axis: $\displaystyle (-1,2)$ and $\displaystyle (7,2)$

    End points of minor axis: $\displaystyle (3,-1)$ and $\displaystyle (3,5)$

    Length of latus rectum: $\displaystyle 2\frac{b^2}{a} = 2\frac{(3)^2}{4} = \frac{9}{2}$

    How can I find out the end points of latus rectum? and are my answers right tell now?
    You've got everything right so far. To get the end-points of the latus rectum is very easy. You know that the semi-latus-rectum has length $\displaystyle \frac94$, so just move up and down through this distance from each of the foci, and you get to each of the end points. So one of them will be $\displaystyle (3 + \sqrt7, 2 + \frac94)$. I'll leave the rest to you.

    Grandad
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