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## Main Question or Discussion Point

how do we define the eccenticity of a pair of straight lines

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how do we define the eccenticity of a pair of straight lines

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Eccentricity is a property of conic sections. Two lines do not a conic section make.

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symbolipoint

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yes.

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HallsofIvy

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The eccentricy of such a hyperbola is [tex]\sqrt{ca^2- cb^2}{ca}= \sqrt{a^2- b^2}{\sqrt{c}a}[/tex]. As c goes to 0 that goes to 0. Strictly speaking the eccentricity of a degenerate hyperbola is "not defined" but roughly speaking it is infinity.

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Hurkyl

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I think you have the wrong formula for the eccentricity.

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then what is the correct answer

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HallsofIvy

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[tex]\frac{\sqrt{ca^2- cb^2}}{ca}= \frac{\sqrt{a^2- b^2}}{\sqrt{c}a}[/tex]

and the result is the same as before.

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