I didn't understand why the method works fine to find the parametrization of the cuspidal curve:
I didn't understand why finding these intersections points will give me the whole curve.
thanks
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1do you know what are the level curves for $x^3-y^2=0$? – janmarqz Jan 22 '14 at 20:50
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@janmarqz no I don't know, maybe $y=\lambda x$? – user42912 Jan 22 '14 at 20:54
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1check[ http://www.wolframalpha.com/input/?i=implicitplot+x%5E3-y%5E2%3D%3D0 ] – janmarqz Jan 22 '14 at 20:55
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@janmarqz every point meet some line which passes through the origin, hence we can parametrize the curve by this intersection, am I right? – user42912 Jan 22 '14 at 21:02
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1the level curve $x^3-y^2=0$ intersect the lines $y=\lambda x$, yes, sample [ http://www.wolframalpha.com/input/?i=plot+%5B+%7Bx%5E%283%2F2%29%2C-x%5E%283%2F2%29%2C+x%7D+%5D%2C+%7Bx%2C0%2C1.2%7D ] – janmarqz Jan 22 '14 at 21:12
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1@janmarqz thank you for your help – user42912 Jan 22 '14 at 21:18
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do forget to upvote me :D – janmarqz Jan 22 '14 at 21:23
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@janmarqz it's done :) – user42912 Jan 22 '14 at 22:58