Let "(x, \\quad y=Y)" be the intersection point of the curves
"y=\\sqrt{\\frac xc} \\quad \\perp \\quad Y=Y(x), \\quad x>0, \\quad y>0."
Then
"Y'=-\\frac{1}{y'}=-2\\sqrt{cx}."
But "c=\\frac{x}{y^2}" . Therefore
"Y'=-\\frac{2x}{Y} \\quad \\text{or} \\quad Y^2+2x^2=C."
We set the family of ellipses
"\\frac{x^2}{a^2}+\\frac{y^2}{2a^2}=1."
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