Ae = [ 2 1; 1 2]; // ellipse
Ah = [ 1 4; 4 3]; // hyperbola
Ap = [ 1 1; 1 1]; // parabola
// graph
theta = 0:%pi/50:2*%pi;
n = size(theta,2);
PtsInCol = [cos(theta); sin(theta)];
PrsInRow = PtsInCol';
R2e = zeros(theta);
R2h = zeros(theta);
R2p = zeros(theta);
for i = 1:n, R2e(i) = PrsInRow(i,:)*Ae*PtsInCol(:,i); end;
for i = 1:n, R2h(i) = PrsInRow(i,:)*Ah*PtsInCol(:,i); end;
for i = 1:n, R2p(i) = PrsInRow(i,:)*Ap*PtsInCol(:,i); end;
Re = sqrt(1 ./ R2e);
Rh = sqrt(1 ./ abs(R2h)); // absolute value to avoid complex numbers.
Rp = sqrt(1 ./ R2p);  
scf(1);
clf();
id = color("darkgreen"); // define dark green
polarplot(theta, Re,style=2); //blue
polarplot(theta, Rh,style=5, strf="000"); //red
polarplot(theta, Rp,style=id, strf="000"); //green
legend('Ellipse','Hyperbola','Parallel Lines');
xs2eps(1,'polar.eps');