Question
Prove that the line with equation is a tangent to the ellipse with equation if, and only if, .
HELP!
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,