The given curve is an ellipse, which can be also rewritten as follows

For rate of change of x and y, the given equation can be differentiated with respect to a time variable t

. The rates of change of x and y, if they are equal then 32x+18y =0, which means y= -

Sustituting y= - , in the equation of the ellipse and solving for x, it would give x= . The corresponding y values will be

Hence the required points are and

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