Finding the equation of parabola

[jamescv31]

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.

 

[HallsofIvy]

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).

 

[jamescv31]

Yes the length of latus rectum is 2