You can get the p coordinate (√ 3c, 4 √ 3/c), and OM = (c, 4/c+ 1).
Substitute the m coordinate into the elliptic equation. Eliminate a, and finally get the quadratic equation about b 2 (taking c as a constant).
The equation must guarantee: △ > =0,b^2>; 0。 Then find the range of c: R.
So when c=2, |op| is the smallest.
At this time, b 2 = 12 and a 2 = 16.
So the ellipse: x2/16+y2/12 =1.