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

x = 3sin2ø
y = 3cos2ø


Eliminate The Parameter And Write The Corresponding Rectangular Equation Whose Graph Represents The Curve X 3sin2ø Y 3cos2ø class=

Sagot :

Answer: [tex]\dfrac{x^2}{9}+\dfrac{y^2}{9}=1[/tex]

Step-by-step explanation:

Given

[tex]x=3\sin 2\phi\\y=3\cos 2\phi[/tex]

square and add [tex]x\ \text{and}\ y[/tex] terms i.e.

[tex]\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]\\[/tex]

Using identity [tex]\sin ^2\theta +\cos ^2 \theta =1[/tex]

[tex]\Rightarrow x^2+y^2=9\\\\\Rightarrow \dfrac{x^2}{9}+\dfrac{y^2}{9}=1[/tex]

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