If it's got a positive slope at x = 2, then it's tangent to the bottom side of the ellipse, so let:

<-- This is the ellipse equation solved for y.

So

meaning the tangent line goes through the point .

The tangent line will have a slope equal to the first derivative of y at x = 2:

So the tangent line is:

Using the point gives:

Thus the tangent line is:

-Dan