Question

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Answer 1

Answer: $\dfrac{x^2}{9}+\dfrac{y^2}{9}=1$

Step-by-step explanation:

Given

$x=3\sin 2\phi\\y=3\cos 2\phi$

square and add $x\ \text{and}\ y$ terms i.e.

$\Rightarrow x^2+y^2=[3\sin 2\phi]^2+[3\cos 2\phi]^2\\\Rightarrow x^2+y^2=9\sin ^22\phi+9\cos ^2 2\phi\\\Rightarrow x^2+y^2=9[\sin^2 2\phi +\cos^2 2\phi]$

Using identity $\sin ^2\theta +\cos ^2 \theta =1$

$\Rightarrow x^2+y^2=9\\\\\Rightarrow \dfrac{x^2}{9}+\dfrac{y^2}{9}=1$