syms a b x y k m
eqn1 = x^2/a^2+y^2/b^2==1;
eqn2 = y==k*x+m;
eqns = [eqn1 eqn2];
expr = collect(eliminate(eqns,y))
expr1=eliminate(eqns,y);
p = coeffs(expr1(1),x);
discriminant=simplify((p(2)^2-4*p(1)*p(3)))
[x,y] = solve(eqns,[x,y]);
P1 = [x(1),y(1)];
P2 = [x(2),y(2)];
x1plusx2=simplify(x(1)+x(2))
x1x2=simplify(x(1)*x(2))
y1plusy2=simplify(y(1)+y(2))
y1y2=simplify(y(1)*y(2))
chord_length = simplify(sqrt((x(1)-x(2))^2+(y(1)-y(2))^2))