# Bizarre Hyperbola

Calculus Level 4

The hyperbola above has equation $$2x^2 + 10xy + 8y^2 + 4x + 2y + 1 = 0$$.

Let $$m_{1}$$ and $$m_{2}$$ be the slopes of the asymptotes (shown in green) such that $$|m_{1}| > |m_{2}|$$, and let $$m_{3}$$ be the slope of the line that passes through both points, where the tangents have infinite slopes.

Find the value of $$\dfrac{1}{|m_{1}| - |m_{2}| - |m_{3}|}$$.

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