SOLUTION: How do you exactly solve for the latus rectum of an ellipse?

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Question 624242: How do you exactly solve for the latus rectum of an ellipse?
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
If you're asking about finding the length of the latus rectum of an ellipse, it is:


If you're asking about how to find the endpoints of the latus rectum, then
  1. Determine if the ellipse is vertical or horizontal.
  2. Find the center, (h, k), of the ellipse.
  3. Find the "c" for the ellipse. "c" is the distance from the center of the ellipse to each focus. "c" is often found using the "a" and "b" from the equation of the ellipse and the equation
  4. Find half of the length of the latus rectum. IOW: . We're going to call this number "q" in the next part.
  5. The endpoints of the two latus recti...
    • for a horizontal ellipse: (h+c, k+q), (h+c, k-q), (h-c, k+q) and (h-c, k-q)
    • for a vertical ellipse: (h+q, k+c), (h+q, k-c), (h-q, k+c) and (h-q, k-c)
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