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The curve is given by x^2+2r(sqrt(y))=xy

What is dx/dr when y is constant?

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x^2+2r√y = xy
If y is constant, it's just like any other dumber, so

2x dx/dr + 2√y = y dx/dr
dx/dr (2x-y) = -2√y

dx/dr = 2√y / (y-2x)

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