Is it possible to plot any implicit equation without knowing its x and y limits?

Question

I have an equation: 9 x^2 + 11 y^2 == 68 + 2 Sqrt[3] x y. Can I plot this function in mathematica without giving the {x, , } and {y, , }??

Wolfram|Alpha has some good heuristics for this sort of thing, so one might do WolframAlpha["plot 9 x^2+11 y^2\[Equal]68+2 Sqrt[3] x y"] for example. — Daniel Lichtblau, Aug 22 '18 at 03:43
Possible duplicate of Plotting implicitly-defined space curves — , Oct 02 '18 at 04:49

score 3 · Accepted Answer · answered Aug 21 '18 at 19:43

RegionPlot[
 ImplicitRegion[9 x^2 + 11 y^2 == 68 + 2 Sqrt[3] x y, {x, y}]]

For non-trivial examples, ContourPlot with explicit bounds can be much faster.

You can also find the bounds with functions like MaxValue, e.g.

MaxValue[{x, 9 x^2 + 11 y^2 == 68 + 2 Sqrt[3] x y}, {x, y}]
(* Sqrt[187/6]/2 *)

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