at what points of the ellipse 16x^2 + 9y^2 = 400 does the ordinate decrease at the same rate at which the abcissa increases ??

Let (*x*, *y*) be the required point.

Then

Consider the given curve

......(!)

Differentiate the above function with respect to *x*,

Substitute the value in the above equation, we have

Now substitute, in the equation of the curve (1), we have

Now for the value ,

Now for the value ,

Hence the required points are

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