Elliptical Brain Twister

Sometimes, people need more than 48 hours, before they can find time to play with a post.

(I was interested, but I do things according to my schedule.)
 
From Google's cache:

You are given an ellipse with semi-major axis a = 1, and semi-minor axis b = .6 (given a and b you can derive any other aspect of the ellipse: eccentricity, foci, etc.).

Point T is a tangent point on the ellipse, with its perpendicular partner, line P.
Line F is a 45 degree reference line, drawn from the upper right corner.
Point H is where line P intersects line F.
Line Q is the horizontal distance from point H to the end of the box (x=1). Line Q = 3P (so P = Q/3).

Find the (x,y) coordinates of point T and point H.
Find the length of line P, and the angle between line P and line F (theta).

Good luck! See who can figure it out! And please show how you did it, that is the part I am interested in. Thanks.
Click to expand...
I can't retrieve the image. Sorry. ;)
 
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