76. Parametric equations of the line $x=2 \cos t, y=3 \sin t$, where $0 \leqslant t \leqslant 2 \pi$, convert to an equation with two variables.
Solution. Expressing from the second equation $\sin t=\frac{y}{3}$ and considering that $\cos t=\sqrt{1-\sin ^{2} t}$, we find $\cos t=\sqrt{1-\frac{y^{2}}{9}}$. Next, substituting this expression into the first equation, we have

$$
x=2 \sqrt{1-\frac{y^{2}}{9}} ; x^{2}=4\left(1-\frac{y^{2}}{9}\right) ; \frac{x^{2}}{4}=1-\frac{y^{2}}{9} ; \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 .
$$