Parametric coordinates of an ellipse

1. Mar 1, 2007

chaoseverlasting

1. The problem statement, all variables and given/known data

$$\frac{x^2}{a^2}+\frac{y^2}{a^2(1-e^2)} =1$$

The ellipse meets the major axis at a point whose abscissa is $$\lambda$$. Find lim $$\theta ->0$$.

2. Relevant equations

Parametric coordinates of an ellipse: (acosx,bsinx)

3. The attempt at a solution
The abscissa is the x coordinate and here the x axis is the major axis as $$b^2 = a^2(1-e^2)$$. Therefore, $$\lambda =acos\theta$$.

Which would give you $$a$$. The answer, however, should be ae... dunno how...

2. Mar 1, 2007

AKG

Could you write the problem out exactly as it's given. I find it hard to believe they'd ask you to find $\lim _{\theta \to 0}$ without saying what you're supposed to be finding the limit of as theta goes to 0. Is it the limit of the abscissa of the point on the ellipse at angle theta to the real axis, as theta goes to 0?

3. Mar 1, 2007

HallsofIvy

Staff Emeritus
I'm with AKG! Find the limit of WHAT as $\theta$ goes to 0?

4. Mar 4, 2007

chaoseverlasting

But thats the whole question. Limit of $$\lambda$$ as $$\theta$$ goes to 0. But $$\lambda$$ comes out to be a which is totally independent of theta.

5. Mar 5, 2007

AKG

No, write it out EXACTLY as given.

6. Mar 5, 2007

HallsofIvy

Staff Emeritus
That was NOT what you originally said. You said "Find lim $\theta-> 0$, NOT $lim \lambda as \theta-> 0$!.

Now, tell us how $\theta$ is defined!

7. Mar 12, 2007

chaoseverlasting

What I've written out, IS the whole question. Thats all there was to it. This question came in an exam, and the answer I got is independent of theta. I dont see how it can be anything else! All they're asking for is the point of intersection of the ellipse and the x axis. And thats (a,0).

8. Mar 12, 2007

AKG

You sure you wrote out exactly what was given? They honestly asked you to find "$\lim _{\theta \to 0}$"? They didn't tell you what to find the limit of? They didn't define $\theta$? Assuming that 0 < 1 - e2 < 1 (note that this an assumption, one that should have been made explicit in the question), the major axis is the line segment from (-a,0) to (a,0). It doesn't make sense to speak of the point where the ellipse meets the major axis because it meets it at two different places, (-a,0) and (a,0), and both these points have different abscissae. Thus $\lambda$ isn't even well-defined.

A question has to make sense, i.e. it has to mean something, before you can conceivably find a right answer to it. For the reasons above, this question is far from making sense. So if you're SURE that you've written out the problem EXACTLY as it's given to you, then there's nothing anyone can do to help you because the problem doesn't make sense. Otherwise, WRITE OUT THE PROBLEM EXACTLY AS GIVEN.

9. Mar 13, 2007

chaoseverlasting

Guess the problem doesnt make sense. Must have been a typo in the paper.