Calculating Eccenticity of a Pair of Straight Lines

[lizzie]

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

 

[Vid]

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

 

[Vid]

Exactly.

http://mathworld.wolfram.com/images/eps-gif/ConicSection_1000.gif

 

[lizzie]

but i have read that pair of straight lines is a part of a conic section. how do u define a conic section.

 

[symbolipoint]

Which kind of "pair of lines" do you mean? A pair of intersecting lines can be a conic section (but does this then have an eccentricity?)

 

[lizzie]

yes.

 

[HallsofIvy]

x²/a^2- y²/b^2= 0 is a "degenerate" conic section. It is the limiting case of then hyperbola x²/a²c- y²/a²c= 1 or x²/a²- y²/b²= c as c goes to 0 and, since it can be factored as (x/a- y/b)(x/a+ y/b)= 0, its graph is the two lines x/a- y/b= 0 and x/a+ y/b= 0.

The eccentricy of such a hyperbola is $$\sqrt{ca^2- cb^2}{ca}= \sqrt{a^2- b^2}{\sqrt{c}a}$$. 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.

 

[Hurkyl]

I think you have the wrong formula for the eccentricity.

 

[lizzie]

then what is the correct answer

 

[HallsofIvy]

Just bad "LaTex". I had meant
$$\frac{\sqrt{ca^2- cb^2}}{ca}= \frac{\sqrt{a^2- b^2}}{\sqrt{c}a}$$
and the result is the same as before.