// Plot Quad plots the conic section for a given 2x2 symmetric matrix
// It assumes that the matrix is A and it is already defined.
// It plots black curves
theta = 0:%pi/50:2*%pi; // %pi is scilab for the constant pi
n = size(theta,2); // theta is a 1 x n row vector
x = zeros(theta); // x and y start as zero vectors
y = zeros(theta);
for i = 1:n,
    angle = theta(i); // this angle
    c = cos(angle);
    s = sin(angle);
    X = [ c, s ];
    r = sqrt(1/abs(X*A*X')); // formula from section 4
    x(i) = r*c; // r cos(theta)
    y(i) = r*s;
end;
plot(x,y,'k-');
a = gca(); a.isoview="on";
title="Conic for A = ["+string(A(1,1))+" "+string(A(1,2)) +"; "+string(A(2,1))+" "+string(A(2,2))+"]";
xtitle(title,"x","y");