Question

eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve x=4costhetay=2sintheta

Answer 1

We have the following trigonometric identity:

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

then, if we calculate the following expression:

$\begin{gathered} x^2+y^2=(4\cos \theta)^2+(2\sin \theta)^2 \\ =16\cos ^2\theta+4\sin ^2\theta \end{gathered}$

as we can see, the coefficients 16 and 4 gives us the lenght of the axis of the ellipse, therefore, the rectangular equation that eliminates the parameter is:

$\frac{x^2}{16}+\frac{y^2}{4}=1$