See this thread for some general comments about ellipses that should help with this problem. Remember that the eccentricity is given by .
Take P to be the point . Then (see the link in my other comment above) the normal at P has equation .
Put y = 0 in that equation to see that N is the point . Put x = 0 to see that G is the point .
Then use the usual distance formula to see that .
Therefore , and so .