math help

[madah123]

i have amath question i couldnt solve in 3 hours.
its to find the equation of acircle that touch the three points
(2,0) -(0،-12) - (6،8)
by using the general form of the equation
x^2+Y^2+ax+by+c=0

each time i tried to solve it .
the equation applied to the first and the second point but not the third

[madah123]

I tried solving it like this:
-.- the point (2،0) is on the circle .-. it fulfils the equation
x^2+y^2+ax+by+c=0 .-.
2^2+0^2+2a+0y+c=0
4+2a+c=0
2a+c=-4 ---->1
--------------------------------------------------------------------------------------------------------------
-.- the point (0،-12) is on the circle .-. it fulfils the equation
x^2+y^2+ax+by+c=0 .-.
0^2+-12^2+0+-12b+c=c
144-12b+c=0
-12b+c=-144 * -1
12b-c=144 ------->2
---------------------------------------------------------------------------------------------------------------------
-.- the point (6،8) is on the circle .-. it fulfils the equation
x^2+y^2+ax+by+c=0 .-.

6^2+8^2+6a+8b+c=0
100+6a+8b+c=0
6a+8b+c=-100 --------->3
------------------------------------------------------------------------------------------------------------------------
then i tried to combine the equations together still i couldnt get the right answer

[NuclearSilo]

it's easy, it's just a system of 3 equation:
answer: a=-71 b=23.5 c=138

[madah123]

Oh my answers were kinda close i got
a= -74.375
b=24.0625
c=144.75

[takolin]

x²+y²+ax+by+c=0

Points: (2,0) (0,-12) and (6,8)

Fill in each point in the equation.

2²+0²+2a+0b+c = 0
0²+(-12)²+0a-12b+c=0
6²+8²+6a+8b+c=0

"Reduce" them.

2a+c+4=0
-12b+c+144=0
6a+8b+c+100=0

Now you need to solve those 3 equations in order to know what a,b and c is. And you'll have the equation for your circle.

The most easy solution for the 3 equations would be a making a matrix and reduce it.
But I can't be arsed doing it without my calculator.

[madah123]

x²+y²+ax+by+c=0

Points: (2,0) (0,-12) and (6,8)

Fill in each point in the equation.

2²+0²+2a+0b+c = 0
0²+(-12)²+0a-12b+c=0
6²+8²+6a+8b+c=0

"Reduce" them.

2a+c+4=0
-12b+c+144=0
6a+8b+c+100=0

Now you need to solve those 3 equations in order to know what a,b and c is. And you'll have the equation for your circle.

The most easy solution for the 3 equations would be a making a matrix and reduce it.
But I can't be arsed doing it without my calculator.

And how is that diffrent than what i did ?
I have no problems with making the 3 equation i have problems with combining them

[takolin]

What do you mean with combine.

You found the 3 equations like I did.
You just failed to solve them. I can't help you with that one, ask your math-teacher.

http://www.easycalculation.com/matrix/m ... lgebra.php

A nice shortcut if you don't have a calculator near you. It won't teach you the basics of solving equations though, but it makes things quicker if you know how to do so.



Edit:

A small help in how to solve it.

2a+c=-4
<=>
a = (-4-c)/2

12b -c = 144
<=>
b = (144+c)/12

Now substitute a and b in the 3rd equation.
Now you only have 1 parameter (c).
Find a solution for c.
Find a and b by filling in c in the 2 equations I gave you.

[madah123]

I will post exactly what i did so tell where i did wrong
2a+c=-4
+
12b-c+144
=
2a+12b=140 *3
=
6a+36b=420
-
6a+8b+c=-100
=28b-c=520
+
2a+c=-4
=2a+28b=516 *3
=6a+84b=1584
--------------------------------------
6a+8b+c=-100
+
12b-c=144
=
6a+20b=44
---------------------------------------------
=6a+84b=1584
-
+a+20b=24
=
64b=1504
b=24.0625

12b-c=144
288.75-c=144
c=144.75
2a+c=-4
2a+144.75=-4
a=74.375
_____________________________________________________________________
i rechecked it alot of times i cant see where i went wrong

[NuclearSilo]

woa woa, what's with this wall of code.
Try simply add/sub the equation 3 and 1, 3 and 2 you'll get 2 equation with a and b. After that is a piece of cake.

[takolin]

woa woa, what's with this wall of code.
Try simply add/sub the equation 3 and 1, 3 and 2 you'll get 2 equation with a and b. After that is a piece of cake.

My method is easier imo.
In the end you have 1 equation with 1 unknown figure.

Or just use a matrix. My calculator solves those as well.

[Riptide]

Seriously the key to math problems is to think simple, your thinking to complex. Keep it simple and focus on the problem before you. Don't start thinking to deep.

[DonBebek]

Too bad I absolutely despise math-.-

[JustaDude]

You need to study more dude, that was one easy question indeed.

[bryanvan]

Seriously the key to math problems is to think simple, your thinking to complex. Keep it simple and focus on the problem before you. Don't start thinking to deep.

My teachers tells me everything that I have that prob XD that I think way to difficult, thats why mostly I got the most difficult questions right and and the really easy ones wrong.

[Riptide]

Seriously the key to math problems is to think simple, your thinking to complex. Keep it simple and focus on the problem before you. Don't start thinking to deep.

My teachers tells me everything that I have that prob XD that I think way to difficult, thats why mostly I got the most difficult questions right and and the really easy ones wrong.

Though problems require easy solutions!