Parametric Quadratic

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If we create a parametric curve where both x and y are quadratic in t, and inspect its implicit equation, we see that it is a conic.

To see if it is a parabola in general, we rotate the parametric curve to make its axis vertical. The angle of the axis of the parabola can be used to work out how to rotate the original curve so that it aligns with the axes. We see that the resulting equation, although very long (so it is not shown), contains Y terms but no XY or Y^2, and is this a parabola.

Expressions

Name Input
Angle Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image