Finding the equation of parabola

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SUMMARY

The discussion focuses on determining the equation of a parabola given the directrix x = -1, axis y = 2, and a latus rectum of length 2. The vertex of the parabola can be calculated as either (-1/2, 1) for a parabola opening in the positive x direction or (-3/2, 1) for a parabola opening in the negative x direction. The relationship between the latus rectum and the distance from the vertex to the focus is established, confirming that the distance is 1/2. This analysis provides a clear method for finding the vertex and the corresponding equations of the parabola.

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jamescv31
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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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