This is the second definition of ellipse. The long axis of ellipse E is a=2 and the focal length is c=√3, so the equation is:

x^2/4

+

y^2= 1；

(2) Let the slope of the straight line be k and the coordinates of c and d be (x 1, y 1), (x2, y2);

Then the L equation is: y=kx-2, substitute it into the elliptic equation and find the product of two roots: x1* x2 =12/(4k2+1);

Similarly, substitute x=(y+2)/k into the elliptic equation and find the product of two roots y1* y2 = (4-4k2)/(4k2+1);

Vector oc od = 0；; Then x1* x2+y1* y2 = 0; It is found that k=2 or -2,

So the equation of the straight line L is y=2x-2 or y=-2x-2.