There are then cases: Then line and the ellipse have only point in common, and is a tangent. The tangent direction has perpendicular vector , so the tangent line has equation for some . Because is on the tangent and the ellipse, one obtains . Then line has a second point in common with the ellipse, and is a secant.
There are th.en cases: Then line and the ellipse have only point in common, and is a tangent. The tangent direction ,has perpendicular vector , so the tangent line has equat.ion for some  Because is on the tangent and the ellipse, one obtains . Then line has a second point in common with the ellipse and is a secant