Question

A particle is moving along the ellipse 16x^2+9y=144.
Find all points
(x, y) on the ellipse at which the rates of change of x and y with respect to
time are equal. You may assume that dx/dt and dy/dt are never both zero
at the same time.. @Calculus1

Answer 1

are you sure you have the equation of the ellipse correct?
shouldn't the y be y^2?

Answer 2

ya sry

Answer 3

ok, so we can re-arrange this as:\[(\frac{x}{3})^2+(\frac{y}{4})^2=1\]which in polar coordinates would be:\[x=3\cos t\]\[y=4\sin t\]so:\[dx/dt=-3\sin t\]\[dy/dt=4\cos t\]we want the rates of change to be equal, so:\[-3\sin t=4\cos t\]\[\tan t=-4/3\]can you work out the rest from there?