It is more clear if we rewrite your code as follows:
b = 1/3;
f[{x_, y_}] := Power[b*(x), 3/2] - Power[1.65, 0.5]*b*(x) + (b*(y))^2;
ContourPlot[f[{x, y}] == 0, {x, -20, 20}, {y, -20, 20},
PlotPoints -> 100,
MaxRecursion -> 1
]
This produces your original figure, but we have defined an explicit function f
, for convenience.
Now we can define the geometric transformation that rotates your figure about {0,0}
by 105° and then moves it by {-10, 5}
in the (x,y) plane.
tf = RotationTransform[105 Degree, {0, 0}]@*TranslationTransform[-{-10, 5}];
Now
ContourPlot[f[tf@{x, y}] == 0, {x, -20, 20}, {y, -20, 20},
PlotPoints -> 100,
MaxRecursion -> 1
]
gives your desired result.
b
is not defined in your code. I assumeb = 1/3
? $\endgroup$b
just make plot bigger, I edited question. $\endgroup$