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Math Help - Latus rectum

  1. #1
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    Post Latus rectum

    How do u find the two points that define the latus rectum? With the Focus at (0,-7) and the directrix line y=7.
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  2. #2
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    Quote Originally Posted by Jmoney008 View Post
    How do u find the two points that define the latus rectum? With the Focus at (0,-7) and the directrix line y=7.
    The latus rectum is the line which passes through the focus and is parallel to the directrix.

    The equation of the parabola is:

    4 \cdot (-7) \cdot y = x^2~\implies~\boxed{y=-\frac1{28} x^2}

    The latus rectum is placed on the line l: y = -7.

    To determine the endpoints of the latus rectum calculate the coordinates of the intersection points between the parabola and the line l.
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  3. #3
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    Quote Originally Posted by earboth View Post
    To determine the endpoints of the latus rectum calculate the coordinates of the intersection points between the parabola and the line l.
    If I remember correctly the equation for the latus rectum is the absolute of 4p. That gives the length and the rest is obviously self explanatory.
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