Question

Write the equations of the two asymptotes

Answer 1

\[(\left( y+3^{} \right)^{2}\div9)- (\left( x-2^{} \right)^{2}\div16) = 1\]

Answer 2

i think rhs wud be 0 ns lhs is same

Answer 3

this is a hyperbola with center (-3,2)
the slopes of the asymptotes will be \(\large \pm \frac{b}{a} \) where b=4, a=3.
to get the equation use these slopes and the center to get point-slope form.

Answer 4

Slope = rise/run
m = 3/4
y = ±3/4x + b
-3 = ±3/4(2) + b
b = -3/2 and b = -9/2
y = 3/4x - 9/2
y = -3/4x - 3/2

Answer 5

((y+3)2÷9)−((x−2)2÷16)=0

Answer 6

our slopes seem to differ @Calcmathlete ....

Answer 7

lemme double check mine...

Answer 8

Really? I always remembered it as rise/run because people taught it differently all the time.

Answer 9

3x+4y+6=0
-3x+4y+18=0

Answer 10

my bad... slope should be \(\large \pm \frac{3}{4} \) as @Calcmathlete says...:)

Answer 11

Yeah. For some reason, everyone teaches which one is a and which one is b differently...some say a is always negative, some say a is always with x, and it's just confusing. THis way, I can figure it out with out them.

Answer 12

i thought this was a left/right branch hyperbola... it turns out the the positive term is y^2 so this is an up/down branch hyperbola....

Answer 13

Yeah.

Answer 14

im gonna give my teacher a headlock.

Answer 15

lol

Answer 16

I gotta go to bed. :/ See ya.

Answer 17

Thanks so much!