The parametric equations of the circle $x^2+y^2+2 x-4 y-4=0$ are

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

Solution

Given equation of circle is $\begin{aligned} & x^2+y^2+2 x-4 y-4=0 \\ & \Rightarrow\left(x^2+2 x+1\right)+\left(y^2-4 y+4\right)-4-5=0 \\ & \Rightarrow(x+1)^2+(y-2)^2=3^2 \end{aligned}$ $\therefore \quad$ Parametric equation of circle is $x=-1+3 \cos \theta, y=2+3 \sin \theta$

Asked in: MHT CET 2023 (10 May Shift 2)

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