<s>[INST] Show that $x^2+y^2$ is constant for all values of $\theta$. Given that $x=3\sin \theta-2 \cos \theta$ and $y=3\cos \theta+2 \sin \theta$
i)Find the value of the acute angle $\theta$ for which $x=y$
ii)Show that $x^2+y^2$ is constant for all values of $\theta$.
My attempt, 
$3\sin \theta-2 \cos \theta=3 \cos \theta+2 \sin \theta$
$\sin \theta=5 \cos \theta$
$\sin \theta-5 \cos \theta=0$
$\tan \theta-5=0$
$\theta=78.7$
How to solve question ii?
 [/INST] hint: $x^2+y^2 = 9(\cos^2 \theta+\sin^2\theta)+4(\sin^2\theta + \cos^2\theta) = ....$
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