Question

What are the asymptotes of the hyperbola with the equation 9y^2-4x^2=36? Graph the hyperbola.

Answer 1

I already put it in standard form

Answer 2

pretty much like the last one right? btw no one likes these conic section questions i noticed
they are not that hard

Answer 3

and I have an idea what it looks like.. what are asymptotes?

Answer 4

\[y=\pm\frac{a}{b}x\]

Answer 5

that is of course the form if it is
\[\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\]

Answer 6

so... I'm kinda confused.

Answer 7

what general form did you get?

Answer 8

after dividing by 36 that is

Answer 9

\[\frac{ y^2 }{ 4}+\frac{ x^2 }{ 9 }=1\]

Answer 10

with a minus sign not a plus sign right?

Answer 11

that means \(a=2,b=3\)

Answer 12

asymptotes are
\[y=\frac{2}{3}x\] and
\[y=-\frac{2}{3}x\]

Answer 13

yes, my bad

Answer 14

ohhh.... okay :) so it's the slope?

Answer 15

and the y-intercepts are \[(0,\pm2)\] right?

Answer 16

@satellite73