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Math Help - analytic geometry about ellipses

  1. #1
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    analytic geometry about ellipses

    Give the equation of the ellipse having foci at (-1, -1) and (-1, 7) and the length of the semi - minor axis is 8 units.
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  2. #2
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    Hello fishlord40
    Quote Originally Posted by fishlord40 View Post
    Give the equation of the ellipse having foci at (-1, -1) and (-1, 7) and the length of the semi - minor axis is 8 units.
    The centre of the ellipse is at the mid-point of the line joining the foci. So that's at (-1, 3). This means the equation will be of the form:
    \frac{(x+1)^2}{a^2}+\frac{(y-3)^2}{b^2}=1
    The axis is along the line x = -1, so the major axis is vertical, having foci where y = 3 \pm be, b being the length of the semi-major axis and e the eccentricity. This gives:
    be = 4
    The length of the semi-minor axis is the value of a. So a = 8.

    Finally, with an ellipse with a vertical major axis, we have:
    e^2 = 1-\frac{a^2}{b^2}
    Eliminate e to find b, and hence the equation of the ellipse.

    Grandad
    Last edited by Grandad; February 15th 2010 at 01:54 AM. Reason: Correction - I didn't read the question properly!
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