
06513067
j
2016a.00588
Berendonk, Stephan
Proving the reflective property of an ellipse.
Math. Mag. 87, No. 4, 276279 (2014).
2014
Mathematical Association of America (MAA), Washington, DC
EN
G40
tangent to an ellipse
reflective property
exterior angle bisector
doi:10.4169/math.mag.87.4.276
Summary: The tangent to an ellipse at a point $P$ can be constructed as the exterior angle bisector of the angle that the point $P$ makes with the two foci of the ellipse. Typically this fact is proved by showing that the exterior angle bisector cannot meet the ellipse in a second point, and therefore must be the tangent. This note gives an alternative proof that is more in line with the notion of tangent as a limit of secants.