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I have a function of $4$ variables: (distance function) $$d(x,x_1,y,y_1)=(x−x_1)^2+(y−y_1)^2$$ subject to $2$ constraints:

  1. $\frac{(x+h)^2}{a^2}+\frac{(y+k)^2}{b^2}= 1$

  2. $\frac{(x_1+h_1)^2}{a_1^2}+\frac{(y_1+k_1)^2}{b_1^2}= 1$

Using Lagrange multipliers, what are the values of $x$, $x_1$, $y$ and $y_1$ in terms of $h$, $k$, $a$, $b$, $h_1$, $k_1$, $a_1$, and $b_1$?

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    I typset your equations in TeX to make them easier to read - can you check I didn't introduce any mistakes? Mainly in the definition of $d$, you had (x-x1)2, so I assumed the 2 was a ^2.2012-09-10
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    No it is all as it is meant to be. What is TeX? Can I download it from somewhere? Thanks by the way:)2012-09-10
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    @ David Hoffman: in optimization problems, constraints are either equalities or inequalities. Your "constraints" are neither. You may want to take a look at http://www.lyx.org2012-09-10
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    Both of them are equal to 1. Sorry.2012-09-10
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    @ David Hoffman: shouldn't the variables be only $x$ and $y$, and the rest be mere parameters? Also, do you have numerical values for the parameters?2012-09-10
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    @DavidHoffman You don't have to download anything, essentially just put maths in $ signs. See http://meta.math.stackexchange.com/questions/5020/tex-latex-mathjax-basic-tutorial-and-quick-reference for more information.2012-09-10
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    All four of them are variables because I am trying to express minumim distance between 2 ellipses. There is no fixed point thus no specific parameters, just symbols.2012-09-10

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