Ellipse Tangents

1
Ellipse Tangents

• How to find the point where a given focal ray
  intercepts an ellipse, and construct the
  tangent-line at that point

2
Finding the point-of-tangency
Given the angle a
Construct point A so its distance from focus F1
equals major-axis Construct the perpendicular
bisector of the segment from A to F2 Point T is
where that bisector meets the line-segment from A
to F1
A
T
a
axis
F1
F2
3

Proving the Reflection Property
Angle BTF1 equals angle CTA (these are
vertical angles) Angle CTA equals angle CTF2
(angles in congruent triangles) Thus
angle-of-incidence BTF1 equals
angle-of-reflection CTF2
B
A
T
C
axis
F1
F2
4
Angle relationships
Angle d equals one-half of angle g
A
T
d
g
B
d
d
a
b
a
axis
F1
F2