No, it is not.
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A curve. It would be called a parabolic curve.
simple curve is a curve which doesnot cross itself,it neednot be closed....... but a simple closed curve is a curve which is simple and also closed. every simple closed curve is a simple curve but not vice versa.
It depends on where arc XY is: on a circles, a parabola or some other curve; and what else you know about the curve.
A Parabola.
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.