maths 3 advanced

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an experimental satelite is placed into a polar ellipical orbit above the earth. both its apogee and perigee are above the equator and the earths centre is the focus of the ellipical orbit. the earths radius is taken ar 6000km. the furthest point of the satellites orbit is 10000km from the earths surface and the nearest approach is 2000km. determine the height of the satellite above each pole.

  • maths 3 advanced -

    ignoring all those pesky zeros, we can set up the ellipse as follows:
    center of earth at (0,0)
    perigee at (-8,0)
    apogee at (16,0)
    center at (4,0)

    so, the equation is

    (x-4)^2/a^2 + y^2/b^2 = 1

    plugging in our points, we have
    144/a^2 + 0 = 1
    a = 12
    a^2-c^2 = b^2
    b^2 = 12^-4^2 = 128

    so our equation is

    (x-4)^2/144 + y^2/128 = 1

    Now find the polar altitude (when x=0) ...

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