When I am ask to parametrize all solutions can I just give the answer or do I have to proove that my parametrization is good?
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You have to go $2$ ways to prove that your parametrization works. $(1)$ You have to make sure all solutions can be parametrized this way and $(2)$ you have to make sure all values obtained from the parametrization are solutions. – Joshua Wang Nov 14 '20 at 17:18
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Further to @JoshuaWang's (2), it involves being specific about the set of allowed values for the parameters. For example, if you specify a circle in the plane of centre $(a,,b)$ and radius $r$, $a,,b\in\Bbb R$ and $r\in\Bbb R^+$. – J.G. Nov 14 '20 at 17:21