Math Is Fun Forum

juan

Banned

hyperbola

Let f(x) be a function such that on putting any value of x we get the equation of a hyperbola which is conjugate of the hyperbola having x as eccentricity.

then find, f(f(f(f(x)))

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: hyperbola

hi juan,

I'm confused by your question.

x as eccentricity.

f(x) => x is a variable but x as eccentricity => x is a constant.

Please check the wording of your question.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: hyperbola

Hi bob

I think the wording might be correct. E.g.:

For x=2 f(x) will be conjugate to a parabola with eccentricity 2.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: hyperbola

hi Stefy,

As I understand the term 'conjugate hyperbola', first you have a hyperbola, then you have another hyperbola that has it's axes interchanged.

That would imply that f(x) is a hyperbola and so it has a single value for it's eccentricity, lets call it 'e'.

You can then have a second hyperbola, conjugate to the first with the same eccentricty.  But I still don't see how you can have an infinity of hyperbolas, covering every value that x might take.

If f(x) isn't a hyperbola, then you cannot have a conjugate hyperbola.  It would be like having the transpose of a matrix without having the matrix first.

Bob

graphs courtesy of Wiki.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: hyperbola

Hi Bob

I got (x**2-1)*x**2-y**2=b**2. I am confused.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: hyperbola

Don't get what you mean by **

I've just read some more on this.  The eccentricity of a hyperbola and its conjugate are only the same if the asymptotes are at right angles.

see stretched graphs. (ignore scales ... should have fixed the axes and just stretched the curves)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: hyperbola

Hi bob

** <=> ^

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: hyperbola

??

Is that your answer to the question or what?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: hyperbola

I am not sure what it is. I got that somehow,but it doesn't look possible.

The incident with bobby has happened again.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: hyperbola

The incident with bobby has happened again.

Mind telling me what incident you are talking about?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Raito

Member

Registered: 2012-04-27

Posts: 50

Re: hyperbola

What has happened,bobbym?