Why Does My Ellipse Tangent Calculation Lead to Infinity?

[KV-1]

1. Homework Statement , is best expressed in the photograph, as this is a fairly detailed problem:
[PLAIN]http://img833.imageshack.us/img833/3972/pleasehelp.jpg
2. all equations included in the image
3. the attempt at the solution is in the image as well

When I take the limit of that last equation, I get a nonsensical answer--infinity. I am well sure that its not infinity. If anything, it must be negative infinity.

What am I doing wrong? Is it my simplification? Is there a strategic error?

Please help!

Found the same question here with some searching:
http://expresshelpline.com/support-question-6498190.html

the answer is not given, but that's a different approach, the person used the y=mx+b way.

 

[Mark44]

I didn't check your work, but there seems to be something wrong with your last line:
h(c) = (a² - c²)/c + c
This simplifies to
h(c) = (a² - c² + c²)/c = a²/c.

From your drawing, c is positive, and a² is positive, so h(c) should be positive, but the point on the y-axis is clearly negative. I suspect that you were not as careful as you need to be with the choice of pos/neg square roots in your preceding work.

 

[KV-1]

Hah,
It's actually (b^2-a^2)/b for the answer... don't know why, but the y-mx+b yielded the correct answer... less room for mistakes there!

thanks a lot though Mark44