The parametric equations of the circle $x^2+y^2-6 x-2 y+9=0$ are

The parametric equations of the circle $x^2+y^2-6 x-2 y+9=0$ are
  1. $x=1+\cos \theta, y=3+\sin \theta$
  2. $x=3+\cos \theta, y=1+\sin \theta$
  3. $x=3+\sin \theta, y=1+\cos \theta$
  4. $x=3+\sin \theta, y=1+\cos \theta$

Solution

$\begin{aligned} & x^2+y^2-6 x-2 y+9=0 \Rightarrow(x-3)^2+(y-1)^2=1^2 \Rightarrow x-3=\cos \theta \quad \text { and } \\ & y-1=\sin \theta \end{aligned}$ Hence, parametric equation is $x=3+\cos \theta$ and $y=1+\sin \theta$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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