Hyperbola proof (1 Viewer)

[Sunyata]

From a point P on x^2/a^2 - y^2/b^2 = 1, two lines are drawn parallel to each of the asymptotes, cutting the asymptotes at M and N. Prove that the area of the parallelogram ONPM is constant (where O is the origin).


How the hell do I do this? I found the equ. of the lines and found M and N BUT when I try to use the area of a parallelogram to prove its constant...it gets all messy and crap.

Please show me how to do this?

NP: bx+ay-bx1 - ay1 = 0
MP: bx-ay-bx1+ay1=0
N[(bx1+ay1)/2b , (bx1+ay1)/2a]
M[(bx1-ay1)/2b,(ay1-bx1)/2a]

 

[fullonoob]

From a point P on x^2/a^2 - y^2/b^2 = 1, two lines are drawn parallel to each of the asymptotes, cutting the asymptotes at M and N. Prove that the area of the parallelogram ONPM is constant (where O is the origin).


How the hell do I do this? I found the equ. of the lines and found M and N BUT when I try to use the area of a parallelogram to prove its constant...it gets all messy and crap.

Please show me how to do this?

NP: bx+ay-bx1 - ay1 = 0
MP: bx-ay-bx1+ay1=0
N[(bx1+ay1)/2b , (bx1+ay1)/2a]
M[(bx1-ay1)/2b,(ay1-bx1)/2a]

if asymptotes are y = +-x how can parallel lines cut each other?

 

[khorne]

Perhaps he means cutting the other asymptote

 

[fullonoob]

Perhaps he means cutting the other asymptote

ahh i see got ya
you can do it :L
i have work to do