# It's algebra or calculus or something else?

Calculus Level 5

Consider all pairs of real values $$(p,q)$$ that satisfy

$p^{2} + q^{2} +13 = 8p + 2q.$

The maximum and minimum value of

$\sqrt{p^{2} + q^{2} -2p + 6q +9}$ are $$M$$ and $$m$$ respectively. Find the value of $$4(\frac{M}{m})^{2}$$.

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