Parametrization for implicit function

Question

$3y^2=x(1-x)^2$

By differentiation we can knwo that the sketch of this graph has one circle.

I want to draw a graph in maple. Implicit plot does not work well

So I will use parametric way.

Please give me a parametrization.

Why not just solve for $y$ and plot the resulting two curves? — aschepler, May 21 '14 at 03:11
@aschepler seems like your comment is an answer now, maybe it's worth putting it as an answer... — James S. Cook, May 21 '14 at 03:30

score 1 · Accepted Answer · answered May 21 '14 at 15:15

Polynomial equations in two variables can be plotted like this

algcurves[plot_real_curve](3*y^2 - x*(1-x)^2, x, y);

Maple plot

You can improve the plots returned by implicitplot by including the gridrefine option:

plots:-implicitplot(3*y^2 = x*(1-x)^2, x= 0..2, y= -1..1, gridrefine= 3);

A parameterization of a polynomial curve can be obtained by

algcurves[parameterization](3*y^2 - x*(1-x)^2, x, y, t);

Maple responds:

[3*t^2/(t^2-2*t+1), -t*(-1+2*t+2*t^2)/(-3*t^2+3*t+t^3-1)]

1 Answers1