Question

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

x = 3sin2ø
y = 3cos2ø

Answer 1

Answer:
`(x^2)/(9)+(y^2)/(9)=1`

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 (x^2)/(9)+(y^2)/(9)=1`