MHB Finding the equation of parabola

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The discussion focuses on finding the equation of a parabola given the directrix x = -1, axis y = 2, and a latus rectum of length 2. The vertex is determined to be either (-1/2, 1) or (-3/2, 1), depending on the direction the parabola opens. The distance from the vertex to the focus is calculated as 1/2, which corresponds to the latus rectum being four times that distance. The analysis confirms that the length of the latus rectum is indeed 2. The conversation emphasizes the importance of understanding the relationship between the vertex, focus, and directrix in parabola equations.
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Greetings, I‘m trying to analyze the given of directrix x = -1, axis y = 2, and latus rectum as 2

I believe there‘s two possibility equations.

I‘m not sure for finding the vertex since I got between ( -.5, 0) and origin itself.
 
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I presume that, by "latus rectum as 2", you mean that the length of the latus rectum is 2. In a parabola that is always 4 times the distance from the vertex to the focus so that distance is 1/2. that is also the distance from the vertex to the directrix so the vertex must be at (-1+ 1/2, 1)= (-1/2, 1) (with the parabola opening in the positive x direction) or at (-1- 1/2, 1)= (-3/2, 1) (with the parabola opening in the negative x direction).
 
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Yes the length of latus rectum is 2
 
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