Height of an ellipse above the plane in three dimensions (z parameter)

[jmm5872]

Homework Statement

What is the expression for z (the height above the xy-plane) in terms of r,f,w,i.

r = the distance
f = the angle between the semi-major axis and the r vector
w = the angle that the semi-major axis makes with the y-axis
i = the angle that the plane of the ellipse makes with the xy-plane

This is actually an Astronomy problem, where the ellipse is the orbit of an asteroid and the xy-plane is the plane of the solar system (planetary orbital plane).

Homework Equations

The Attempt at a Solution

I started by parametrizing the ellipse with respect to one of the foci:

x = c+r*cos(f)
y = r*sin(f)
z = (c+r*cos(f))tan(i)

This doesn't seem correct, or complete I guess. I'm not sure how w comes into play? w rotates the ellipse relative to the y-axis but I can't picture where it should go?

 

[AvroArrow]

I feel like I'm missing something simple but I can't seem to figure it out. Any help would be appreciated!