# How to paint over the ParametricPlot Ellipse?

I want to paint over the ellipse. I have following

a = 2;
b = 1;
ellipse[a_, b_][t_] := {a*Cos[t], b*Sin[t]}
ellipse[a, b][10]
ParametricPlot[{ellipse[a, b][t]}, {t, -10, 10}]


How can i paint over this area? I was trying to use some options of parametric plot, but without success. Help please! Tnx

• Try RegionPlot instead of ParametricPlot. – Will.Mo Nov 20 '17 at 12:03
• How can I use region plot if I have only parametric function ellipse? – Mykhailo Voloshyn Nov 20 '17 at 12:10
• Using ParametricRegion but for performance sake you should calculate parameters and use Circle. – Kuba Nov 20 '17 at 12:18
• Thanks. I was trying using ParametricRegion, and the ellipse is painted, but how to paint over the area? I have an error. – Mykhailo Voloshyn Nov 20 '17 at 12:49
• Graphics[{LightBlue, Opacity[0.75], Disk[{0, 0}, {a, b}]}, Axes -> True] or Graphics[{Circle[{0, 0}, {a, b}], LightBlue, Opacity[0.75], Disk[{0, 0}, {a, b}]}, Axes -> True] – Bob Hanlon Nov 20 '17 at 13:46

You can introduce an extruding parameter within ParametricPlot or ParametricRegion.

### ParametricPlot:

ParametricPlot[r ellipse[a, b][t], {t, 0, 2π}, {r, 0, 1}]


### ParametricRegion:

Region @ ParametricRegion[r ellipse[a, b][t], {{t, 0, 2π}, {r, 0, 1}}]


ParametricPlot is used for visualization only, whereas ParametricRegion can be used for more than just visualization -- it's a region. You can query mathematical properties like area, centroid, point membership, etc.