2 variables in 2 quadratic equations in excel

[[email protected]]

Dear ms excel user/programmers:

I hope this question is not repeated before. But anyway

highly appreciate anyone can tell me how (or hint) to use ms excell
and/or visual c/c++, basic, or octave(emulate matlab) to solve:
(12-x)^2 + y^2 =15^2,
(16+y)^2+x^2=25^2

(by programming or using its built in function)?

that ^2 mean square.

looking to any excel user, mathmatician, and/or programmer's help,
eric, [email protected]

[Steve Dalton]

Hi Eric

The brute force way (requiring the least mathematical analysis) is to
calculate the left hand side as functions of two reasonable first guess x
and y inputs and then calculate the total error (say as a sum squares of the
differences) of these compared to the right hand sides.

Once you have that you can run the solver add-in to minimise (or set to
zero) the error cell's value by altering (subject to optional constraints)
your input x and y values.

Regards

Steve Dalton


<[email protected]> wrote in message
news:[email protected]...
> Dear ms excel user/programmers:
>
> I hope this question is not repeated before. But anyway
>
> highly appreciate anyone can tell me how (or hint) to use ms excell
> and/or visual c/c++, basic, or octave(emulate matlab) to solve:
> (12-x)^2 + y^2 =15^2,
> (16+y)^2+x^2=25^2
>
> (by programming or using its built in function)?
>
> that ^2 mean square.
>
> looking to any excel user, mathmatician, and/or programmer's help,
> eric, [email protected]
>

[Dana DeLouis]

> and/or ...octave(emulate matlab) to solve:

I don't have matlab, but I would assume there is a Solve command similar to
the following.
Are you looking for a more general form of the equation in order to solve
other equations with different variables?

equ =
{
(12-x)^2 + y^2==15^2,
(16+y)^2 + x^2==25^2
};

Solve[equ]

{x -> 0, y -> 9},
{x -> 24, y -> -9}

HTH
--
Dana DeLouis
Win XP & Office 2003


<[email protected]> wrote in message
news:[email protected]...
> Dear ms excel user/programmers:
>
> I hope this question is not repeated before. But anyway
>
> highly appreciate anyone can tell me how (or hint) to use ms excell
> and/or visual c/c++, basic, or octave(emulate matlab) to solve:
> (12-x)^2 + y^2 =15^2,
> (16+y)^2+x^2=25^2
>
> (by programming or using its built in function)?
>
> that ^2 mean square.
>
> looking to any excel user, mathmatician, and/or programmer's help,
> eric, [email protected]
>

[Dana DeLouis]

Just be advised that, in general, two circles may not intersect (two
imaginary solutions), have 1 common point, or hopefully in your example, two
real solutions...

http://mathworld.wolfram.com/Circle-...ersection.html

HTH
--
Dana DeLouis
Win XP & Office 2003


"Dana DeLouis" <[email protected]> wrote in message
news:[email protected]...
>> and/or ...octave(emulate matlab) to solve:
>
> I don't have matlab, but I would assume there is a Solve command similar
> to the following.
> Are you looking for a more general form of the equation in order to solve
> other equations with different variables?
>
> equ =
> {
> (12-x)^2 + y^2==15^2,
> (16+y)^2 + x^2==25^2
> };
>
> Solve[equ]
>
> {x -> 0, y -> 9},
> {x -> 24, y -> -9}
>
> HTH
> --
> Dana DeLouis
> Win XP & Office 2003
>
>
> <[email protected]> wrote in message
> news:[email protected]...
>> Dear ms excel user/programmers:
>>
>> I hope this question is not repeated before. But anyway
>>
>> highly appreciate anyone can tell me how (or hint) to use ms excell
>> and/or visual c/c++, basic, or octave(emulate matlab) to solve:
>> (12-x)^2 + y^2 =15^2,
>> (16+y)^2+x^2=25^2
>>
>> (by programming or using its built in function)?
>>
>> that ^2 mean square.
>>
>> looking to any excel user, mathmatician, and/or programmer's help,
>> eric, [email protected]
>>
>
>

[AlfD]

Hi!

It's not difficult to check whether solutions will be real etc.

Take the quoted example:

The centres of the circles are (12,0) and (0,-16) respectively and their radii are respectively 15 and 25.

The distance between the centres is 20 (nice of you to choose easy numbers!).
For the solutions to be real the distance between the centres must be not greater than the sum of the radii. Your chosen example obviously meets this requirement. This is generalisable in Excel terms.

For the actual solution I would work with axes such that the x-axis coincides with the line of centres of the circles and the origin is on the chord joining the points of intersection of the circles. It's easier starting from this end, with the aim of rotating/translating from this special case to the general one later.

More later, maybe

Alf

[AlfD]

Hi!

Yes: there's some useful stuff at http://mathforum.org/dr.math/
Enter intersecting circles in the search box

Alf