Analytic Geometry

Ellipse and Foci

Sum of distances from foci = 2a

  • High school
  • about 4 min
  • 2 of 7 in the family
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F₁F₂d₁=35d₂=285P
a = 160
b = 100
Angle of P
\ racx2a2+\ racy2b2=1\ rac{x^2}{a^2} + \ rac{y^2}{b^2} = 1
d1+d2=35.1+284.9=320.0=2a=4.0⋅80d_1 + d_2 = 35.1 + 284.9 = 320.0 = 2a = 4.0 \cdot 80

An ellipse = set of points where the SUM of distances from two foci F₁ and F₂ is constant (= 2a). Move point P and watch d₁+d₂ stay constant.