This function gives points of intersection of line and ellipse. Given major axis (a), minor axos (b),
center (O(h,k)) of ellipse and two points (A(x1,y1), B(x2,y2)) lying on the stright line. This function gives two points
of intersection C1 and C2. If the line and ellipse doesn't intersect, intersections points return NaN's.

a = randperm(10,1); % some random major axis
b = randperm(10,1) ; % some random minor axis
% if a = b, we get circle
O = rand(2,1) ; % random center of ellipse

A = rand(1,2) ; B = rand(1,2) ; % Two random points for stright line

[C1,C2] = lineEllipse(a,b,O,A,B) ; % GEt intersection poins

%% plot
th = linspace(0,2*pi) ;
x = O(1)+a*cos(th) ;
y = O(2)+b*sin(th) ;

figure
plot(x,y)
hold on
plot(A(1),A(2),'.r')
plot(B(1),B(2),'.r')

plot(C1(1),C1(2),'*k')
plot(C2(1),C2(2),'*k')

L = [A ; B ; C1 ; C2] ;
plot(L(:,1),L(:,2),'g')
axis equal