There is no specific name for it since the curve is not specified. The curve could be a conic section (circle, ellipse, parabola, hyperbola), or a trigonometric function, or a polynomial, exponential, etc. Or a combination of these.
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No, a line is not a polygon. A polygon is a closed plane area bounded by straight sides. A line, by itself, does not contain an area.
A geometrical curve is defined as any set of points. Therefore, counter-intuitively, a straight line is also a geometrical curve.
It's a "LINE" or a "CURVE"
Yes, but not a straight line.
There is no kind of shape that has a straight line or curved line a kind of element of the following question is "space"...hope this helps