Answer with explanation:
We are given a parametric equation as:
[tex]x=3 \sin^3 t[/tex]
and [tex]y=3 \cos^3 t[/tex]
Hence, we can represent our equation as:
[tex]\sin^3 t=\dfrac{x}{3}\\\\\\\sin t=(\dfrac{x}{3})^{\dfrac{1}{3}}\\\\\\Hence,\\\\\sin^2 t=(\dfrac{x}{3})^{\dfrac{2}{3}}\\\\and\ similarly\\\\\cos^3 t=\dfrac{y}{3}\\\\\cos t=(\dfrac{y}{3})^{\dfrac{1}{3}}\\\\Hence,\\\\\cos^2 t=(\dfrac{y}{3})^{\dfrac{2}{3}}[/tex]
As we know that:
[tex]\cos^2 t+\sin^2 t=1[/tex]
Hence, on putting the value in the formula we get the equation in rectangular coordinates as:
[tex](\dfrac{x}{3})^{\dfrac{2}{3}}+(\dfrac{y}{3})^{\dfrac{2}{3}}=1[/tex]
Hence, this is a equation of a ASTROID.
