Proving Triangle Area of Curve x^2-2y^2=4 Constant

[Nima]

Prove that the triangle formed by the asymptotes of the curve with equation x^2 - 2y^2 = 4 and any tangent to the curve is of constant area.

Thanks. :)

 

[matt grime]

Homework? Well, the answer is do it: find the equations of the asymptotes, and a tangent and voila do it.

 

[Nima]

I'm having problems finding the asymptotes.

 

[Nima]

Could anyone help me do this Q? Thanks.

 

[Nima]

Please could someone show me how to do this Question? I'm having difficulties, because I've barely been taught this chapter and I want to at least see how such a question is answered. Thanks.

 

[TenaliRaman]

You have to let us know what u have done?
Post whatever working u have done(even if its wrong its fine), since that would help us to pitch the answer at the right frequency.

-- AI

 

[Nima]

You have to let us know what u have done?
Post whatever working u have done(even if its wrong its fine), since that would help us to pitch the answer at the right frequency.

-- AI

I really don't know where to start, I don't know how to find the asymptotes of the curve, that's a key problem...

 

[TenaliRaman]

Ok u need to run through the basics a bit then.
First of all,
the equation u have is a hyperbola
Read abt hyperbolas here,
http://colalg.math.csusb.edu/~devel/precalcdemo/conics/src/hyperbola.html

Asymptotes are mentioned in this article and its also explained how they are obtained.
I will leave the rest to you for now. Try to go ahead and solve your original problem. If u are getting stuck again, post your working.

-- AI

 

[mathwonk]

for starters, the asymptotes of xy = 1 seem to be the x and y axes y=0 and x=0, [take derivative of y = 1/x, get -1/x^2, and let x go to infinity, so the slope goes to zero, or let x go to zero, and the slope goes to infinity] so after rotating axes, the asymptotes of uv = (x-y)(x+y) = 1, are probably the lines u=0 and v=0, i.e. x = y and x = -y.

you might look at this to be sure, as I am allergic this type of thing.