The cartesian equation of the curve given by $x=6 \cos \theta, \quad y=6 \sin \theta$ is

The cartesian equation of the curve given by $x=6 \cos \theta, \quad y=6 \sin \theta$ is
  1. $x^{2}+y^{2}=36$
  2. $x^{2}+y^{2}=5$
  3. $x^{2}+y^{2}=25$
  4. $x^{2}+y^{2}=6$

Solution

On squaring and adding both given equations, we get $\begin{aligned} x^{2}+y^{2} &=36 \cos ^{2} \theta+36 \sin ^{2} \theta \\ &=36\left(\cos ^{2} \theta+\sin ^{2} \theta\right) \\ x^{2}+y^{2} &=36 \end{aligned}$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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