The line is tangent to .

There are two conditions:

1. The line and the ellipse must have a common point (x,y)

2. Their slopes must be equal at (x,y)

The slope of is m.

And the ellipses is,

(Implicit differentiation)

(Some algebra)

As the slopes are equal, we can write

Plug this is

Then plug it in

Plug the x we found before,