Question

Write the equation of a hyperbola with vertices (0, -5) and (0, 5) and co-vertices (-2, 0) and (2, 0)

Answer 1

Here is a very good site that will explain how the various components in the equation of a hyperbola fit together: http://www.mathsisfun.com/geometry/hyperbola.html

have a look through this and, if you still need help, then let me know and I will try and help you further.

Answer 2

ok..ill try to work it out i guess

Answer 3

look also here: http://jwilson.coe.uga.edu/emt668/EMAT6680.2004.SU/Stein/6690/conic_sections_files/summary.htm

the hyperbola is defined as the 3rd curve down. It contains all the components that your question mentions.

Answer 4

ok so would i be looking for a horzontal or vertical graph

Answer 5

if you look carefully at the forms of the two types of hyperbola, then you should conclude that yours must be one with a Vertical Transverse Axis.

Answer 6

ok, would it be (x-0)^2/2^2+(y-5)^2/0^2 ?

Answer 7

no - are you sure you solved for the vertical hyperbola?

Answer 8

yes..well tried

Answer 9

its equation is given by:\[\frac{(y-k)^2}{a^2}+\frac{(x-h)^2}{b^2}=1\]and its vertices are at:\[(h,k-a),(h,k+a)\]and its co vertices are at:\[(h-b,k),(h+b,k)\]

Answer 10

look at the information given to you and let me know what you get for the values of a, b, h and k

Answer 11

im confused on the a^2

Answer 12

first, look at the equations for the vertices of this hyperbola and form some relationships with the data given to you in your question

Answer 13

e.g. you are told that the vertices are at (0, -5) and (0, 5)

therefore you can say that:

(h,k-a) = (0,-5)
(h,k+a) = (0, 5)

Answer 14

now compare each part of the coordinate pairs to establish some relationships

Answer 15

lets just take the first one:

(h, k - a) = (0, -5)

what does that tell you about h? what must it equal?

Answer 16

h,k+a?

Answer 17

if (a, b) = (c, d)

then it implies a = c
and b = d

so, if (h, k - a) = (0, -5)

then h = ?

Answer 18

0

Answer 19

correct, now use the same techniques to find the other values (k, a and b)

Answer 20

(y-0)^2?

Answer 21

please list the values you have found for h, k, a and b

Answer 22

h=0, k - a) = (0, -5)

Answer 23

you need to use all the information given to you to find values for h, k, a and b.

I showed you how to do the first part where I equated the equations for the vertices to the coordinates of the vertices given to you in the question.

you need to do the same now with the co vertices.

Answer 24

(h−b,k),(h+b,k) = -2,0 2,0

Answer 25

can you please explain what you are doing?

Answer 26

I want to see if I can spot where the confusion lies

Answer 27

?

Answer 28

Im writing the co vertices

Answer 29

yes, but I asked you to use these to solve for h, k, a and b - but instead you just list the relations

Answer 30

lets try from the beginning - step by step...

Answer 31

what are the coordinates of the vertices that have been given to you in this question?

Answer 32

(0,-5) and (0,5)

Answer 33

good.

now what are the coordinate of the vertices of a vertical hyperbola in terms of h, k, a and b?

Answer 34

(I listed these for you up there ^^^)

Answer 35

(-2,0)?

Answer 36

no, the vertices will be at:

(h,k-a) and (h,k+a)

Answer 37

It is very late where I am at so I need to go now - maybe someone else can try to explain this to you.

Answer 38

can you not just give me the answer before you get off? im sorry im reallly slow...but i have to have this problem done :/

Answer 39

sorry - the aim of this site is to teach - not just give out answers.

it doesn't matter if you are slow - you need to persevere and try to understand the concepts here otherwise you will never understand how to solve these.

anyway - good luck...

Answer 40

k bye.