\(\displaystyle x \ = \ 3sin(\theta), \ x^{2} \ = \ 9sin^{2}(\theta), \ sin^{2}(\theta) \ = \ \frac{x^{2}}{9}.\)
\(\displaystyle y \ = \ 4cos(\theta), \ y^{2} \ = \ 16cos^{2}(\theta). \ cos^{2}(\theta) \ = \ \frac{y^{2}}{16}.\)
\(\displaystyle Ergo, \ \frac{x^{2}}{9} \ + \ \frac{y^{2}}{16} \ = \ sin^{2}(\theta) \ + \ cos^{2}(\theta) \ = \ 1, \ an \ ellipse.\)
