Chapter 3.10, Problem 30E

To determine

(a)

The quadrants for that $\frac{dx}{dt}>0$.

To determine

(b)

The relation between $\frac{dx}{dt}and\frac{dy}{dt}$.

To determine

(c)

The rate is the $x-\text{coordinate}$ changing when the particle passes the point $\left(1,1\right)$ if its

$y-\text{coordinate}$ is increasing at a rate of $6\text{m/s}$.

To determine

(d)

Find $dy/dt$ when the particle is at the top and bottom of the ellipse.