Question

5. Consider a particle moving counter-clockwise around the ellipse
x^9/9 +y^2/4 = 1. Find a relationship
between
dy/dt
and
dx/dt
What are the rates of change of y and x at the times when the other variable isn't .
changing at all?

Answer 1

x^2/9 + y^2/4 = 1
or
4x^2 + 9y^2 = 36
8x dx/dt + 18y dy/dt = 0
so
dy/dt = - 8x dx/dt / 18y

and dy\x/dt : dx/dt = 4x : -9y

Just think about your last part of the question.

Suppose the x is not changing at all, which would mean of course that dx/dt = 0
what do you think would happen to y ?

Answer 2

if dx/dt = 0 then y should also be zero

Answer 3

@ reiny if dx/dt = 0 then y should also be zero