plotting implicitly defined curve

Hello! I'm trying to solve a problem but I am completly stuck!

I am supposed to plot a curve (I believe using the polar function) that is implicitly defined by x^2+y^2=1+a(sin(xy))^2

where a is 0, 1, 2, 3, 4, 5 I am asked to use the polar coordinates: x = rcos(theta) y = rsin(theta)

r>0 & 0<=theta<=2pi

I am supposed to plot all 6 curves (using different a-values) in the same picture but thats quite simple to do using a loop at the end. The only leads Im given is that I should use fzero to solve and that it might be a good idea to solve for the radius as a function of the angle.

Thanks for any help/input!

Answer 1

[Adam Filion]

If you just need the plot then:

figure; hold on;
for ii = 1:6
    ezplot(['x^2+y^2=1+' num2str(ii) '*(sin(x*y))^2'])
end