Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2016-04-07 13:12:08

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.

Offline

#2 2016-04-07 18:29:00

ElainaVW
Member
Registered: 2013-04-29
Posts: 580

Re: Algebra (2?) Problem

Hello,

Offline

#3 2016-04-08 09:53:23

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.


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.

Offline

#4 2016-04-08 10:52:32

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!

Offline

#5 2016-04-08 12:52:13

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.

Offline

#6 2016-04-09 05:59:22

ElainaVW
Member
Registered: 2013-04-29
Posts: 580

Re: Algebra (2?) Problem

Hello,

What did I do wrong? sad

Offline

#7 2016-04-09 06:08:14

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.

Offline

#8 2016-04-09 06:10:15

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)

Offline

#9 2016-04-09 06:11:56

ElainaVW
Member
Registered: 2013-04-29
Posts: 580

Re: Algebra (2?) Problem

Do you think that Geogebra used a least squares fit?

Offline

#10 2016-04-09 06:13:40

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.

Offline

#11 2016-04-09 06:23:35

ElainaVW
Member
Registered: 2013-04-29
Posts: 580

Re: Algebra (2?) Problem

I missed the post too sad Thanks Relentless.

I didn't simplify sad

I know about Confucius I told you that.

Offline

#12 2016-04-09 06:25:53

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.

Offline

Board footer

Powered by FluxBB