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 { l }_{ 1 } and l 2 { l }_{ 2 } be the lengths of each line. Find the correct expression for

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

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

Note: e is the eccentricity of the ellipse.

a b d c

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