I'm interested in constructing a curvilinear coordinate system with coordinate axes being these two curves: $$x=a, \qquad y^2+x=b,$$ where $a, b$ are parameters that specify the families of the curve, and points on this coordinate can be described by $(a,b)$. Is that something possible? Given two curves, what are some conditions such that they can form a coordinate system?
2026-03-25 19:03:56.1774465436
Can the two curve $x=a$, $y^2 + x=b$ form a coordinate system?
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