Matlab Plotting roots (zeros and poles) of Z-Transform - matlab

Question

I need to plot the roots onto a transfer function H(z) overlaying a unit circle, giving enough room to see all points. I'm able to get the roots from H(z) when it is given in the form zeros = [z0 z1 z2...], poles = [p0 p1 p2]. Using Matlab's roots function, I'm able to get the pole and zero locations. My Matlab code so far is
function zplot(b, a)
b_roots = roots(b);
a_roots = roots(a);
hold on
rectangle('Position',[-1 -1 2 2],'Curvature',[1 1]);
plot(b_roots,'x blue');
plot(a_roots,'o blue');
axis %need axis to be equal and +10percent of maximum value
hold off
end
So far, I can plot the roots and the unit circle, but I need help with adjusting the axes so that they are 1) equal to each other and 2) 10% more than the highest value. I'm not sure how to go about doing this part. I tried making a variable lim_max = max(b_roots,a_roots) but it ended up being an array, and wouldn't work in the axis([-lim_max lim_max -lim_max lim_max]) function. I need the plot to scale to +10% with the inputs as they change.
Side note (not necessary): is there a way for it to look like a circle when I plot it, because right now it ends up looking like an oval most of the time. I can readjust the screen, which is fine, but if there's an easy way to do that, I'd also like to know.

Answer 1

Set axis equal and calculate min/max:
function zplot(b, a)
b_roots = roots(b);
a_roots = roots(a);
xlimits = [min(min([real(a_roots);real(b_roots)])), max(max([real(a_roots);real(b_roots)]))];
ylimits = [min(min([imag(a_roots);imag(b_roots)])), max(max([imag(a_roots);imag(b_roots)]))];
hold on
rectangle('Position',[-1 -1 2 2],'Curvature',[1 1]);
plot(b_roots,'x black');
plot(a_roots,'o blue');
axis equal;
xlim(1.1*xlimits);
ylim(1.1*ylimits);
hold off
end

Answer 2

Use the following code. This will 1) find the maximum overall limits of x and y axes 2) set those limits equal to each other 3) plot those limits +10%
b_roots = roots(b);
a_roots = roots(a);
x_min = min(min([real(a_roots);real(b_roots)]));
x_max = max(max([real(a_roots);real(b_roots)]));
y_min = min(min([imag(a_roots);imag(b_roots)]));
y_max = max(max([imag(a_roots);imag(b_roots)]));
%get the magnitude of the overall minimum value
min_lim = abs(min(x_min,y_min));
%abs may not be necessary
max_lim = abs(max(x_max,y_max));
%set high and low limits equal to each other from negative to positive
eq_limit = [-max(min_lim,max_lim),max(min_lim,max_lim)];
hold on
rectangle('Position',[-1 -1 2 2],'Curvature',[1 1]);
plot(b_roots,'x black');
plot(a_roots,'o blue');
axis equal;
xlim(1.1*eq_limit);
ylim(1.1*eq_limit);
hold off
Thanks to #M.S. for their answer and help.