# Parallel and perpendicular, part 2

Calculus Level 4

$\begin{cases} x^2+y^2=1 \\ x^2-2xy+3y^2 =k\end{cases}$

The above two curves touch each other at $$k=a$$ and $$k=b$$ where $$a>b$$.

Let the area enclosed between the two curve be $$M$$ and $$m$$ for the case $$k=a$$ and $$k=b$$ respecively. Find the value of $$\left\lfloor{\dfrac{1000M}{m}}\right\rfloor$$.

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