Latus RectumDate: 08/08/2002 at 16:17:39 From: Michelle Subject: Latus rectum Dr. Math, I'm working on quadratic equations, and I'm trying to find the definition, an explanation, a formula, or anything that will help me to better understand what exactly latus rectum is. So far all I have been able to find is that when using the formula (x-h)=4p(y-k), the latus rectum is equal to 4p. I don't understand, and any explanation would be wonderful! Thank you. Michelle Date: 08/08/2002 at 23:36:18 From: Doctor Peterson Subject: Re: Latus rectum Hi, Michelle. I would think your book would define the term; but then, I've just been searching the Web for a picture of a parabola that shows the latus rectum, and I can't seem to find any! It's so simple and visual, there's no reason not to show it; I'll let you draw it yourself. Just find a picture of a parabola that shows the focus and either the axis or the directrix, or both. Now draw a line through the focus that is parallel to the directrix (that is, perpendicular to the axis). It will look something like this: o |F o --o-----------o-----------o-- A o | o B o | o oV | | --------------o-------------- d D The vertex is V(h,k), the focus is F, the axis is the line DF, the directrix is the line d, and the line segment AB is the latus rectum, which is Latin for "straight side." Its length is 4p in your equation 4p(y-k) = (x-h)^2 where p is the focal length DV=VF. That is, the semi-latus rectum FB is the same length as FD. If you think about the definition of the parabola, you will see why that has to be true. Here is one of many pages that show a parabola, including the focus and directrix, from Eric Weisstein's MathWorld: http://mathworld.wolfram.com/Parabola.html Here 'a' is used where you use 'p', so don't let that confuse you. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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