Manipulate a plot with display of a condition

This is a how to question --- the example is without importance. I want to manipulate the plot of say a x^2 + b y^2 for (a,b) belonging to a specific set, but a + b > 0. Is it possible to make appear the sum a+b at a specific position in the plot ?

• Notihing I have no idea how to begin. I know how to dispose two image side by side with Row but I don't know how to do what I want. – cyrille.piatecki Apr 27 '16 at 7:12

I am posting the answer based on taking the phrase "the example is without importance" on face value (i.e. not a homework or similar).

I am not exactly I understand the aim.

So, with these caveats and to motivate clarification:

f[a_, b_, x_, y_] := {a, b}.{x^2, y^2} /; a + b > 0
f[a_, b_, x_, y_] := Null
Manipulate[
Column[{
Row[{"a+b= ", a + b}, BaseStyle -> {FontFamily -> "Arial", 20}],
Row[{ContourPlot[Evaluate@f[a, b, x, y], {x, -1, 1}, {y, -1, 1},
PerformanceGoal -> "Quality", ImageSize -> 300],
Plot3D[Evaluate@f[a, b, x, y], {x, -1, 1}, {y, -1, 1},
MeshFunctions -> (#3 &), Mesh -> {{0.1, 0.2, 0.5}},
MeshStyle -> Red, PerformanceGoal -> "Quality",
ImageSize -> 300]}]
}, Alignment -> Center],
{a, -1, 1, Appearance -> "Labeled"}, {b, -1, 1,
Appearance -> "Labeled"}]


• Nearly what I was expecting but is it possible with a+b over the contour plot and if possible with --- Latex fonts – cyrille.piatecki Apr 27 '16 at 8:21
• @cyrille.piatecki I am not sure whether you asking me a cosmetic change or if I misunderstand your aim. The contours are values of $a x^2+b y^2$. In either situation, I suggest you adapt the code above or just use it as a launching point for your own code. The best way to learn Mathematica is playing around. Good luck. :) – ubpdqn Apr 27 '16 at 8:25
• The only thing is that I want the condition inside the plot. – cyrille.piatecki Apr 30 '16 at 10:49