Problem:
Solution:
Part (a) is trivial given exercise 8, we already know to parametrization of the curve $ y^2 = cx^2 - x^3 $, just replace $ (x, y) $ by $ (z ,x) $ we get what we want.
For part (b) is just as simple, we replace $ y $ by $ u $ and set $ c = y^2 = u^2 $, then we are done.
For any point on the surface, $ y $ must be either positive, 0 or negative. In any case, we reduce to a particular curve $ x^2 = cz^2 - z^3 $, now we know by problem 8 part (c) that the parametization covers the whole curve, so the parameterization cover all points on the surface!
Solution:
Part (a) is trivial given exercise 8, we already know to parametrization of the curve $ y^2 = cx^2 - x^3 $, just replace $ (x, y) $ by $ (z ,x) $ we get what we want.
For part (b) is just as simple, we replace $ y $ by $ u $ and set $ c = y^2 = u^2 $, then we are done.
For any point on the surface, $ y $ must be either positive, 0 or negative. In any case, we reduce to a particular curve $ x^2 = cz^2 - z^3 $, now we know by problem 8 part (c) that the parametization covers the whole curve, so the parameterization cover all points on the surface!
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