How to plot an ellipse?

Question

I'm new to Mathematica, and I'm finding it difficult to plot an ellipse. I tried using

Plot[(x/5)^2 + (y/3)^2 == 1, {x, -5, 5}, {y, -3, 3}]

but I'm getting some errors. Is there something wrong with the syntax? Or do I need to rewrite the equation and plot?

Answer 1

Please see this reference: How To | Create Plots.

You need ContourPlot for that implicitly defined function.
You will also need AspectRatio -> Automatic if you want it to look like an ellipse and not a circle.

ContourPlot[(x/5)^2 + (y/3)^2 == 1, {x, -5, 5}, {y, -3, 3}, AspectRatio -> Automatic]

If you merely want to display an ellipse use Graphics:

Graphics[Circle[{0, 0}, {5, 3}]]

Notice that AspectRatio -> Automatic was not needed; it is the default for Graphics, whereas plot functions default to 1/GoldenRatio.

Answer 2

Even though Mr. Wizard's answer plus comments give the most generalizable answers, the closest to what the original question was doing is probably this:

Plot[y /. Solve[(x/5)^2 + (y/3)^2 == 1], {x, -5, 5}, 
 AspectRatio -> Automatic]

The ability to plot two branches of a solution as a single curve is sometimes cited as one of the advantages of the fact that Plot doesn't automatically evaluate its arguments due to its HoldAll attribute (which in other situations causes confusion when you try to plot lists of functions in different colors). Here we want both branches of the square root to appear in the same plot style, and this is automatically recognized. If I had forced the Solve output to be evaluated too early, this plot wouldn't work.

Answer 3

ParametricPlot[{2*Sin[x], Cos[x]}, {x, 0, 2*Pi}]