<s>[INST] Solving these two equations simultaneously I'm having a hard time to solve these two equations simultaneously. I'm arriving to a very long equation..
$$x_0^2+y_0^2=(7\sqrt{2})^2=98$$
$$\sqrt{25+(x_0+2)^2}+\sqrt{4+(y_0-5)^2}=7\sqrt{2}$$
 [/INST] Use polar coordinates $(x,y) = (-r \sin \theta, r \cos \theta)$ to get $r=\sqrt{98}$ and
$$ \sqrt{98 \cos^2 \theta - 2 \sqrt{98} (5) \cos \theta + (-2)^2 + (5)^2} + \\
\sqrt{98 \sin^2 \theta+2 \sqrt{98} (-2) \sin\theta + (-2)^2 +(5)^2 } = \sqrt{98} $$
Numerically there are two solutions at $\theta=28.27437°$ and $\theta=45°$ for the solutions
$$ (x_0,y_0) = ( -4.6893, 8.7184 ) \\ (x_0,y_0) = ( -7, 7 ) $$
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