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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