ellipse problem (1 Viewer)

[c0okies]

PQ is a diameter of the ellipse x^2+4y^2=9. If the eccentric angle of P is pie/3, find the coordinate of P. What is the eccentric angle of Q? Find the coordinates of the corresponding point on the auxiliary circle. Show that the tangents at P and Q are parallel?

Thanks ahead for any help.

 

[Trev]

Haven't come across a question like this before, but this is what I make of it:
x²+4y²=9
x²/9+y²/(9/4)=1
So a=3 and b=3/2
The x coordinate of P is x=acos(angle)=3cos(pi/3) and y coordinate is bsin(angle)=1.5sin(pi/3).
Eccentric angle of Q would be 180+pi/3 (4pi/3) because the diameter is a 180 degree rotation and it's coordinates would be (-3cos(pi/3),-1.5sin(pi/3)). Whatever that simplifies to.
Just use angle rules to prove it's parallel.

 

[c0okies]

hey.. thanx for the hint but i still cant move on from the auxiliary circle... Dx

 

[Trev]

I forgot to add this diagram I drew when I typed up that stuff: