A particle moves counterclockwise around the ellipse with equation 9x^2 + 16y^2 = 25.
a). In which of the four quadrants in dx/dt > 0? Explain.
b). Find a relation between dx/dt and dy/dt.
c). At what rate is the x-coordinate changing when the particle passes the point (-1,1) if its y-coordinate is increasing at a rate of 6 m/s?
d). Find dy/dt when the particle is at the top and bottom of the ellipse.
The Attempt at a Solution
a). I don't see how I could solve this with differentiation so I drew a picture of the ellipse. If the particle is travelling counter-clockwise, x will be increasing over time in quadrants 3 and 4.
b). Implicitly differentiating for x and y both as functions of t I get
dx/dt = (-32y*dy/dt)/18x
c). Plugging in the values for the above formula...
dx/dt = -32*6/18 = -32/3
d). If the particle is at the top and bottom of the ellipse, then x is zero, and thus dy/dt is zero because
dy/dt = (-18x*dx/dt)/32y = 0 @ x = 0
Just checking if I did this correctly particularly a) as I don't see how I can "explicitly" show that dx/dt > 0 in quadrants 3 and 4 outside of explaining why in English.