Tweak It - Equation of Circle From 3 Points

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April 1st, 2009, 09:13 AM

MrLarkins

The HS Math Teacher

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Tweak It - Equation of Circle From 3 Points

This program works great, but I offer it up for tweaks to make it better/prettier, etc.

Usually in a class with Conic Sections, you are required to write the equation of a circle in standard form that passes through 3 points. This involves plugging the 3 given ordered pairs into the general form for a circe (x^2 + y^2 +Dx +Ey +F=0) and then solving the system of resulting equations. This process can be lengthy.

This program allows the user to input the 3 points, then it inserts then into lists, converts the lists to a single matrix, uses rref() (reduced-row echlon form) to solve the system of equations and then completes the square, and finally spits out the center of the circle (H,K) and the R^2 for the standard form equation (x-H)^2 + (y-K)^2 = R^2

Code:

:Disp "POINT 1:"
:Prompt A,B
:Disp "POINT 2:"
:Prompt C,D
:Disp "POINT 3:"
:Prompt E,F
:ClrList L1,L2,L3,L4,L5
:{A,C,E}->L1
:{B,D,F}->L2
:L1^2->L3
:L2^2->L4
:{1,1,1}->L5
:List>matr(L1,L2,L5,(-L3-L4),[A])
:rref([A])->[A]
:Matr>list([A],L1,L2,L3,L4)
:-L4(1)/2->H
:-L4(2)/2->K
:-L4(3)+L4(1)^2/4+L4(2)^2/4->R
:Disp "H=",H
:Disp "K=",K
:Disp "R^2=", R

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Last edited by MrLarkins : April 1st, 2009 at 09:16 AM.

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December 2nd, 2011, 05:39 PM

Boctroy

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Just what i needed

Last edited by Boctroy : December 2nd, 2011 at 06:11 PM. Reason: Thanks

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December 3rd, 2011, 02:49 PM

Janet Chauvin

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Program

Quote:

Originally Posted by Boctroy

Just what i needed

I tried programming my TI 84 with this program. Did you get it to work?

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December 3rd, 2011, 05:05 PM

tifreak8x

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Quote:

Originally Posted by MrLarkins

Code:

:Disp "POINT 1:"
:Prompt A,B
:Disp "POINT 2:"
:Prompt C,D
:Disp "POINT 3:"
:Prompt E,F
:ClrList L1,L2,L3,L4,L5
:{A,C,E}->L1
:{B,D,F}->L2
:L1^2->L3
:L2^2->L4
:{1,1,1}->L5
:List>matr(L1,L2,L5,(-L3-L4),[A])
:rref([A])->[A]
:Matr>list([A],L1,L2,L3,L4)
:-L4(1)/2->H
:-L4(2)/2->K
:-L4(3)+L4(1)^2/4+L4(2)^2/4->R
:Disp "H=",H
:Disp "K=",K
:Disp "R^2=", R

You don't really need the ClrList command, as storing to the lists as you do eliminates any aspects of the lists and recreates them from nothingness with the values you push into them.

Speaking of storing to the lists, you can easily do {1,1,1->L5 without needing the closing }. Same goes with storing back to the matrix. The -> token automatically closes that out for you.

And you don't need the ending " at the end of the Disp commands at the top. The ones at the bottom of your code needs them, however.

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December 4th, 2011, 07:53 AM

MrLarkins

The HS Math Teacher

Join Date: Oct 2007

Location: Central Arkansas

Posts: 72

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great points....that'll cut some bits from the memory.