\(x = 2 + 4\cos \theta\)
\(y = -1 + 4\sin\theta\)
\(\therefore \cos\theta = \frac{x-2}4\)
\(\sin \theta = \frac{y + 1}4\)
\(\because \cos^2\theta + \sin^2\theta=1\)
⇒ \(\left(\frac{x-2}4\right)^2 + \left(\frac{y + 1}4\right)^2 = 1\)
⇒ \((x^2 - 4x + 4)+ (y^2 + 2y + 1)=16\)
⇒ \(x^2 + y^2 - 4x + 2y - 11 = 0\)
which is cartesian equation of given circle.