Question

The question is "What is one of the vertices of the hyperbola (y+1)^2 - (x+1)^2/4 =1
Please help me and thanks in advance :)

Answer 1

do you know where the center of this hyperbola is?

Answer 2

you're welcome in advance too! ;)

Answer 3

Umm no?? I bearly started taking this class today like for 2 mins :(

Answer 4

How would you find the center?

Answer 5

what does your notes/textbook say about the standard equation of a hyperbola?

Answer 6

the equation tells you the center...

Answer 7

x^2/a^2 -/+ y^2/b^2=1

Answer 8

we need the more general form..
lemme put it up...

Answer 9

\[\large \frac {(x-h)^2}{a^2}- \frac {(y-k)^2}{b^2}=1\]
\[\large \frac {(y-k)^2}{a^2}- \frac {(x-h)^2}{b^2}=1\]

Answer 10

in either case, the center is (h,k).
now can you identify your center?

Answer 11

It would be (1,1) right?

Answer 12

not quite.. it's (-1, -1)

Answer 13

Is that because they were being subtracted?

Answer 14

in the formula, yes... and since your equation is (x+1)^2 you can write it as (x - (-1))^2
understand?

Answer 15

Yes. Thanks make so much more sense now :)

Answer 16

once you have the center, we can find your vertices to answer your question.

Answer 17

So thats when we plug in our vertices into the equation?

Answer 18

well, we need to find the vertices...

Answer 19

the equation actually tells us WHERE the vertices are...

Answer 20

in relation to the center..

Answer 21

Oh I got you :)

Answer 22

Thanks DPALNC":)

Answer 23

first... i wrote down two types of equations... do you know why?

Answer 24

yw...

Answer 25

depends if its vertical or horizantal

Answer 26

horizontal*

Answer 27

correct... what type do you have?

Answer 28

Vertical

Answer 29

correct...

Answer 30

so all you need to know is what is your denominator under the (y+1)^2 term... that is a^2.

what is a^2 and what is a ?

Answer 31

Would it be 4?

Answer 32

that's under the (x+1)^2... what's under (y+1)^2 ?

Answer 33

There is nothing under it.... Would there be like an invisible one?

Answer 34

Or what would take place there?

Answer 35

yes.. invisible 1

Answer 36

so a=1

Answer 37

So now it would be 1,-1

Answer 38

because you said we have the vertical branch hyperbola, from the center of (-1, -1), you go UP 1 and DOWN 1 from the center. can you now give me the coordinates of the vertices?

Answer 39

there's your two vertices...