Calculating Pluto's Orbital Time Above/Below Ecliptic

[Globe199]

I'm trying to determine the length of time Pluto spends above/below the ecliptic. I've got these figures:

semi-major axis: 39.264 AU
semi-minor axis: 34.031 AU
orbital eccentricity: 0.249
approx orbital circumference: 230.85 AU
orbital inclination is 17.142° (I'm thinking this number isn't relevant to this question)

So I guess what I'm asking is, given those figures, how do I determine the "section" of the circumference that is above/below the ecliptic? Or is there additional info I need such as the location of the sun as a focus within the ellipse?

The ultimate goal here is to learn how planetary transits can be calculated. Specifically, I was wondering about a schedule of transits across the sun of planets as viewed from Pluto. Thanks for any assistance.

 

[Janus]

You are also going to need the longitude of perihelion and the longitude of the ascending node.

These are important because they tell you how the orbital inclination is orientated with respect to the major axis of the orbit. In Pluto's case, the they are nearly 90° apart.

You might find this helpful, it has tables of the orbital elements and shows how to use them to calculate planetary positions.

http://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf