$(4$ pts$)$ Consider the ellipse $\frac{x^2}{5^2}+\frac{y^2}{3^2}=1.$

$($a$)$ Sketch the ellipse here.

$($b$)$ The ellipse can be drawn with parametric equations. One of them is given here; Fill in the rest, but assume the curve is traced clockwise as the parameter increases.

$x=5cos(t),0t$

$y=,$

$(2$ pts $)$ Find a Cartesian equation relating $x$ and $y$ corresponding to the parametric equations $x=e^{4t},y=e^{-3t}.$ Write your answer in the form $y=f(x).$ Your answer should simplify in a way that gets rid of $e.$

$y=$

$(4$ pts $)$ Given the parametric equations below, write the derivative $\frac{dy}{dx}$ as a function of $t.$

$x=2t+9$

$y=si{n}^2(3t)$