P is on the ellipse, P 2/A 2+Q 2/B 2 = 1 (1).

k(AM)= k(AP)= & gt； -2b/m=(q-b)/p (2)

mo⊥pb = & gt； k(MO)* k(PB)=- 1 = & gt； -b/m*(q+b)/p=- 1 (3)

(2)/(3) Available

2p/(q+b)=-(q-b)/p, available after finishing.

2p^2+q^2=b^2 (4)

(4)-( 1) * b 2, available

2p^2-p^2*b^2/a^2=0

That is 2 = b 2/a 2.

As you can see, there is b > for ellipse; A, that is, the long axis is on the y axis.

∴e=c/b, then b 2 = a 2+c 2.

2=b^2/a^2=b^2/(b^2-c^2)= 1/( 1-e^2)

The solution is e= 1/√2=√2/2.

∴ Eccentricity of ellipse is e=√2/2.