Question

Find the coordinates of the vertices and foci of the hyperbola ((y-1)^2)) /25 - (x+2)^2 = 1
HELP :(

Answer 1

\[\frac{ (y-1)^2 }{ 25 } - (x+2)^2 = 1\]

Answer 2

im only in 6th grade XD no lie so im going to do the math, brb

Answer 3

I'd suggest you re-write the original equation as follows:

Answer 4

hmmmm, its not { y-1} 2^

Answer 5

is it?

Answer 6

what do you mean Jazzi?

Answer 7

\[\frac{ (y-1)^2 }{5^{2} } - \frac{ (x+2)^2 }{ 1^{2} }= 1\]

Answer 8

To complete the problem I need to find dy/dx at (1, -1) so I substitute x = 1, y = -1 into the equation above to get... wait u said cooranents hmm brb again lol

Answer 9

Compare this equation to the one you typed in originally.

Answer 10

@JazziLeeRiser : This problem does not involve calculus.

Answer 11

@mathmale you got it,

Answer 12

I get what you did now :)

Answer 13

:)

Answer 14

im going to medel u @mathmale

Answer 15

OK, good. We can get a lot of info from this re-written equation for your hyperbola.
Can you look at it and determine the CENTER of y our hyperbola?
Can you use the 5 and the 1 from this re-written equation to draw a rectangular box around the center of your hyperbola?

Answer 16

medial*

Answer 17

Sorry, I don't think I can get the center from the equation. Can you please help me?

Answer 18

Your equation involves (y-1)^2. Thus, the y-coordinate of your center is 1.

Answer 19

is it 1, -2 ?

Answer 20

Your equation involves (x+2)^2. Thus, the x-coord of the center is ... what?

Answer 21

Remember that when you write a point as (a,b), the x-coord comes FIRST and the y-coord comes SECOND. Try again. The center of your hyperbola is ... ?

Answer 22

That's right, sorry! (-2,1)

Answer 23

Right you are.
Now, what information does that 5^2 provide you?

Answer 24

it gives us a^2 ad we need that with the equation c^2=a+b^2 right?

Answer 25

Let me change your wording a bit: "It gives us the value of a, which we will insert into the equation c = a + b." Better check this out on the Internet or in your textbook! There are NO squares here.

Answer 26

a = 5. Yes, I agree.
What is b? b = ?

Please refer to the following:

http://www.purplemath.com/modules/hyperbola.htm

Answer 27

I was looking at the foci equation (c^2=a^2+b^2) my bad!

Answer 28

I was wrong and you were mostly correct: You do need to use a^2, b^2 and c^2. Again, please refer to http://www.purplemath.com/modules/hyperbola.htm

Answer 29

so doesn't a= + - square root of 5 ?

Answer 30

Notice that in http://www.purplemath.com/modules/hyperbola.htm a, b and c are illustrated. Also note that a, b and c as showin in that diagram are positive.

You are thinking of 25, I believe; the sqrt of 25 is 5. But we've already been talking in terms of 5. No need to find the square root of 5.

Answer 31

oh right!

Answer 32

b=1 right?

Answer 33

Referring to the diagram in http://www.purplemath.com/modules/hyperbola.htm ,
a is measured horizontally and is the distance between the center and the vertex. Can you determine the value of a? b is measured vertically and is the distance between the center and the vertex. Can you determine b? Once you have a and b, you can find c.

Answer 34

The diagram shows that a is measured horizontally in this particular problem; therefore, a=1. b is measured vertically and here is 5. Agree or disagree?

Answer 35

Can you now draw y our hyperbola following the example in
http://www.purplemath.com/modules/hyperbola.htm ? Show a=1 and b=5.

Answer 36

I am confused on why a=1 if 25 is a ^2 ?

Answer 37

Use the Draw utility.

Answer 38

I don't need to graph it, I just need to find the coordinates and foci :(

Answer 39

Again, please refer to the example in http://www.purplemath.com/modules/hyperbola.htm.
Is a measured vertically or horiz? Is b measured vertically or horiz?

Answer 40

True, you don't need to graph it, but doing so will make it very obvious where your vertices are.

Answer 41

Oh ok, sorry!

Answer 42

Again, the center is at (-2, 1). If a = 1, and a is a horizontal distance, then what are the coordinates of the right vertex? Next, find the coordinates of the left vertex.

Answer 43

I'm stopping here because OpenStudy says you are offline.