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Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Algebra (2?) Problem

Describe the set of all points P with the following property: there exist points A and B on the unit circle such that AB is parallel to the y-axis and P is on AB with AP = 2PB.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Algebra (2?) Problem

Hello,

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Algebra (2?) Problem

Hi EVW;

You are correct about the ellipse but the equation you have is not. I am getting: x² + 9y² = 1 instead.

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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.

Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Re: Algebra (2?) Problem

Hi bobbym, I figured out how to do the problem, and it's an ellipse with equation x^2+9y^2=1 so you were correct!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Algebra (2?) Problem

Hi;

Glad you figured it out.

---

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.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Algebra (2?) Problem

Hello,

What did I do wrong?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Algebra (2?) Problem

Hi;

Looking at the Gebra work you did it seems you traced point P and that is okay but then you picked 5 arbitrary points from the spreadsheet of the trace and used the "Conic from 5 points" command. This did not work as expected.

You only needed 4 points (0, 1/3),(0,-1/3),(-1,0)(1,0) and then http://www.mathsisfun.com/geometry/ellipse.html

Of course, to convince yourself that this is the wanted answer will require a bit more but I am sure you can do that.

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Algebra (2?) Problem

You didn't do anything wrong. Your equation actually simplifies to bobbym's

Last edited by Relentless (2016-04-09 06:14:39)

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Algebra (2?) Problem

Do you think that Geogebra used a least squares fit?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Algebra (2?) Problem

I do not know but anytime you are using floating point numbers as you did you can expect some problems.

Oh wait, I just saw Relentless' post. He is correct, the two answers are the same. What Gebra did not do was simplify all the way.

In any case, using Gebra was overkill and you know what Confucius says...

---

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.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Algebra (2?) Problem

I missed the post too Thanks Relentless.

I didn't simplify

I know about Confucius I told you that.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Algebra (2?) Problem

I know about Confucius I told you that.

Nope, C.R. Greathouse did.

---

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.