# An Elliptic Relation

Geometry Level 4

Let there be an ellipse centred at the origin. Join a line from each focal point to an arbitrarily selected point (x,y). Let $${ l }_{ 1 }$$ and $${ l }_{ 2 }$$ be the lengths of each line. Find the correct expression for

$\left| { l }_{ 1 } - { l }_{ 2 } \right|.$

a) $$e| x|/2$$
b) $$e| x|$$
c) $$2| x|/e$$
d) $$2 e | x|$$

Note: e is the eccentricity of the ellipse.

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