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:
$\frac{(x+h)^2}{a^2}+\frac{(y+k)^2}{b^2}= 1$
$\frac{(x_1+h_1)^2}{a_1^2}+\frac{(y_1+k_1)^2}{b_1^2}= 1$
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 $b_1$?