Question

[Choose the one correct answer and explain your reasoning.]

Given \(\theta\) in the range \(0\leq \theta < \pi\), the equation \[x^2+y^2+4x \cos\theta+8y \sin\theta+10=0\] represents a circle for

  1. \(0<\theta<\dfrac{\pi}{3}\);

  2. \(\dfrac{\pi}{4}<\theta<\dfrac{3\pi}{4}\);

  3. \(0<\theta<\dfrac{\pi}{2}\);

  4. all values for \(\theta\).