vector and parabola question

hi all I'm having a little trouble with 2 problems.

the first is:

with v being a vector going 3 up and 5 right, find the unit vector in the direciton of v.

the second is:

parabola's focus at (2,1) and vertex at (2,4). Find equation of directrix, two points where latus rectum intersects parabola, and equation of parabola itself.

The first problem I don't know exactly where to start with what is given.

The second problem, from what I've figured or thought to have figured is that it opens downward baesd on focus and vertex points, but not sure as to how to find the rest of the information requested.