hyperbola q (1 Viewer)

[Lexie1001]

hey everyone
this ia question 6c, exercise 32b from the fitzpatrick:

Sketch the following and show that they represent rectangular hyperbolas:
2xy - 3x - y - 2 = 0.

my only problem is putting into hyperbola format so i can sketch it....i tried multiplying everything by y which ended up as:

1/(3x-2) - 2x = -1/y

i don't know how i can simplify that any further, mutliplying by x was just as useless. any help appreciated! thanks

 

[Mando]

Hey hey, lexie
sorry, don't know the answer.
ah well.
hope someone knows
c u

 

[Raginsheep]

2xy - 3x - y - 2 = 0
2xy - y = 3x + 2
y(2x - 1) = 3x + 2
y=(3x + 2)/(2x - 1)

 

[Lexie1001]

wow thats so easy - damn it im dumb! thanks for ur help

 

[_ShiFTy_]

2xy - 3x - y - 2 = 0
2xy - y = 3x + 2
y(2x - 1) = 3x + 2
y=(3x + 2)/(2x - 1)

How can you prove that its a rectangular hyperbola?

 

[Raginsheep]

Winplot and then look at the pretty picture.

or, for the unfun method, find the vertical and horizontal asymptotes and show that they are perpendicular to each other.