The discussion revolves around the locus of a point defined by hyperbolic functions, specifically examining the equation \( x(4y^2 + b^2) = ab^2 \). Participants are analyzing the algebraic manipulation of expressions involving hyperbolic cosines and sines.
Some participants have provided feedback on the clarity of the original poster's work and pointed out potential errors in the algebraic steps. There is an ongoing exploration of the factors involved in the equations, with indications that progress is being made towards understanding the problem.
Participants have noted issues with the quality of the work presented, which may affect the clarity of the discussion. There is an emphasis on ensuring that each step in the algebraic manipulation is correctly represented.
synkk said:show that the locus of the point [itex]\left(\dfrac{a(cosh\theta + 1)}{2cosh\theta},\dfrac{b(cosh\theta - 1)}{2sinh\theta}\right)[/itex]
has equation x(4y^2 + b^2) = ab^2
working: http://gyazo.com/4c96af128d0293bce7f18029c2f54b0d
where have I gone wrong :(
haruspex said:Your 5th and 6th lines each have the form <some expression> = 1. The second should have something other than 1 on the right hand side.
Mark44 said:I have to say that the image of your work is very poor quality. IMO, you are lucky that haruspex took the time to decipher your hard-to-read work. I'm sure that many others wouldn't bother.
You're almost there. Just need to spot a factor.synkk said:[itex]-b^2a^2 + 2ab^2x - b^2x^2 = 4y^2x^2 - 4ay^2x[/itex]
not sure where to go from here
haruspex said:You're almost there. Just need to spot a factor.