Hi

How exactly would I do this?

The normal to the ellipse x^2/a^2 + y^2/b^2 = 1 at P(x1, y1) meets the x-axis in N and the Y-axis in G. Prove PN/NG = (1-e^2)/e^2

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- Feb 23rd 2010, 12:06 AMSunyataEllipse
Hi

How exactly would I do this?

The normal to the ellipse x^2/a^2 + y^2/b^2 = 1 at P(x1, y1) meets the x-axis in N and the Y-axis in G. Prove PN/NG = (1-e^2)/e^2 - Feb 23rd 2010, 12:20 AMOpalg
See this thread for some general comments about ellipses that should help with this problem. Remember that the eccentricity is given by .

- Feb 26th 2010, 03:38 PMSunyata
Hi

I've spent a few days on this but I cant solve it. PLEASE HELP!!! - Feb 27th 2010, 06:56 AMOpalg
I'm not entirely surprised. This is a longer and messier calculation than I would have guessed. Here is an outline of how to do it.

Take P to be the point . Then (see the link in my other comment above) the normal at P has equation .

Put y = 0 in that equation to see that N is the point . Put x = 0 to see that G is the point .

Then use the usual distance formula to see that .

Similarly .

Therefore , and so .