Q90 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics

Parametric equations of the circle $2 x^2+2 y^2=9$ are

  • A
    $x=\frac{3}{2} \cos \theta, y=\frac{3}{2} \sin \theta$
  • B
    $x=\frac{3}{\sqrt{2}} \cos \theta, y=3 \sin \theta$
  • Correct answer
    C
    $x=\frac{3}{\sqrt{2}} \sin \theta, y=\frac{3}{\sqrt{2}} \cos \theta$
  • D
    $x=3 \sin \theta, y=\frac{3}{2} \cos \theta$

Solution

Given circle: $2 x^2+2 y^2=9 \Rightarrow x^2+y^2=\frac{9}{2}$ $\Rightarrow$ Centre is $(0,0)$ and $r=\frac{3}{\sqrt{2}}$ Parametric equation is given by $\begin{aligned} & x=r \cos \theta, y=r \sin \theta \\ & \therefore x=\frac{3}{\sqrt{2}} \cos \theta, y=\frac{3}{\sqrt{2}} \sin \theta \end{aligned}$

Hence, the correct answer is option: 'C'.

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