Show that in the curve \[ y^{2}-3 x y-4 x^{2}+x^{3}+x^{4} y+y^{5}=0 \] the radii of curvature at...
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Show that in the curve
\[
y^{2}-3 x y-4 x^{2}+x^{3}+x^{4} y+y^{5}=0
\]
the radii of curvature at the origin are \( \frac{85}{2} \sqrt{17} \) and \( 5 \sqrt{2} \).
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