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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