Prove that on each branch of a hyperbola the difference

is a constant.

*Proof.* ** Incomplete.**

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Stumbling Robot

A Fraction of a Dot
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Prove that the points on each branch of a hyperbola satisfy a property

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Prove that on each branch of a hyperbola the difference

is a constant.

*Proof.* ** Incomplete.**

let X=(x,y) and N=(1,0). Then XN=x and |ex|<=|a|. Since a0, the difference is -2a. If ex<0, the difference is 2a.