What is the definition of eccentric angle in relation to an ellipse?

[Unicyclist]

I'm revising form my A-levels now and I ran into a bit of problem with a question. It looks easy, but I can't get the answer at the back of the book. Could be a typo, but could be me that's wrong.

Question: The eccentric angle corresponding to the point (2, 1) on the ellipse with equation x^2 + 9y^2 = 13 is \theta. Find \tan \theta

The book isn't very clear on what the eccentric angle is, so could someone maybe explain that to me, please? I understand it as the angle from the middle of the ellipse - in this case the origin - to the point (2, 1). So, \tan \theta would be opposite/adjacent, 1/2. Apparently, it's not.

 

[Dick]

I just looked it up at mathworld. The ellipse can be parametrized as x=a*cos(t), y=b*sin(t) where a and b are the semi-axes. The angle 't' is the 'eccentric angle'.

 

[Unicyclist]

Thank you. I should've done that myself.

 

[SAC]

I just looked it up at mathworld. The ellipse can be parametrized as x=a*cos(t), y=b*sin(t) where a and b are the semi-axes. The angle 't' is the 'eccentric angle'.

Thanks a lot, Dick. This was causing me a lot of pain when I saw a question asking how I would graphically determine it, seeing as I had no idea what the eccentric angle was. Makes perfect sense now, just have to use a circle that contains the ellipse to determine the new angle.

Edit: (oh, and sorry to resurrect this thread, just occurred to me that I shouldn't have done so. I'm just so glad now that I couldn't help it :D)

 

[Dick]

Well, cheers. Just because it takes two years doesn't mean it's not worth announcing you got it. I guess.

 

[SAC]

Oh, I just happened to come across this on Google, so it wasn't long at all for me. Everything is relative.

 

[Dick]

Right, sorry, I confused you with to OP.