How to plot this implicit function? (It's one parameter also changes)

Here Φ also varies.

First i got that it is an implicit function. So, fimplicit should be used. But i'm unable to take Φ varied.

Answer 1

[Torsten]

So you want several implicit plots in different colors for different values of phi ?

Use "fimplicit" in a loop using "hold on" before the loop.

phi = [pi/4 3*pi/8 pi/2 5*pi/8 3*pi/4];
hold on
for i=1:numel(phi)
    fun = @(x,y) y.^4 + y.^2.*(2*x*tan(phi(i))-1) + x.^2.*sec(phi(i))^2;
    fimplicit(fun);
end
hold off

Answer 2

[John D'Errico]

The vertical axis indicates the value of phi.

F3 = @(x,y,phi) y.^4 + y.^2.*(2*x.*tan(phi)-1) + x.^2.*sec(phi).^2;

fimplicit3(F3)
xlabel x
ylabel y
zlabel phi

So at any fixed phi, you will get a simple path through the (x,y) plane, indicating the solution locus for that value of phi.

And for a fixed set of values of phi, you can use fimplicit to get the curves as shown by @Torsten.