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

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

asnaseer · Answer

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

anonymous · Answer

ya sry

asnaseer · Answer

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?