Question

Eliminate the parameter.

x = 3 cos t, y = 3 sin t

Answer 1

\(\bf x = 3cos(t)\qquad \qquad y = 3sin(t)\\ \quad \\ \quad \\
\textit{let us solve first by the cos(t) and sin(t)}\\
x = 3cos(t)\implies\cfrac{x}{3}=cos(t)\\ \quad \\
y = 3sin(t)\implies \cfrac{y}{3}=sin(t)\\ \quad \\
\textit{recall the trig identity of }\quad sin^2(\theta)+cos^2(\theta) = 1\\ \quad \\
\cfrac{x}{3}=cos(t)\qquad \cfrac{y}{3}=sin(t)\qquad sin^2(t)+cos^2(t) = 1\quad thus\\ \quad \\
\left(\cfrac{x}{3}\right)^2+\left(\cfrac{y}{3}\right)^2=1\)

raise both numerator and denominators to their exponent, and you'd end up with an ellipse :)

Answer 2

Thank you very much!!! :D