# Familiarity breeds contempt!

Calculus Level 5

A curve passes through $$(-2,-2)$$ and its slope at the point $$(x,y)$$ is given by $$\dfrac 1 {x\sqrt{x^{2}-1}}$$. Which of the following points the curve also passes through?

• A: $$\ \ \left(-\dfrac{2}{\sqrt{3}}, \ -\dfrac{\pi}{6}-2\right)$$
• B: $$\ \ \left(-\dfrac{2}{\sqrt{3}}, \ \dfrac{\pi}{6}-2\right)$$
• C: $$\ \ \left(-\sqrt{2}, \ -\dfrac{\pi}{12}-2\right)$$
• D: $$\ \ \left(-\sqrt{2}, \ \dfrac{\pi}{12}-2\right)$$
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