Find combinations of two variables in functions which must equal certain value

Is it possible to plot a curve of all the combinations of q=sqrt(z1z2) if q must equal 9 for the interval 0<=z1<=40?

It should look something like this:

Answer 1

[John D'Errico]

Algebra? If we have

q = 9 = sqrt(z1*z2)

then it is trivial.

z1*z2 = 9^2

So the curve is given as

z2 = 81/z1

Plotting is equally trivial.

z1 = 0.25:.25:40;
plot(z1,81./z1,'-');
xlabel z1
ylabel z2

Of course, there are no solutions when z1==0.

Do you want MATLAB to do the thinking for you?

syms z1 z2
>> EQN = sqrt(z1*z2) == 9;

z2 = solve(EQN,z2)
z2 =
81/z1

z2fun = matlabFunction(z2)
z2fun =
  function_handle with value:
    @(z1)8.1e+1./z1
    
fplot(z2fun,[0.25,40])