It is known that the left and right focal points of the ellipse x2a2 + y2b2 = 1 (a > b > 0) are F1 and F2 respectively. If there is an intersection p between the straight line with an inclination angle of 30 ° and the ellipse and the PF2 ⊥ X axis, then the eccentricity e of the ellipse is () A. 33B. 32C. 22D. 23

It is known that the left and right focal points of the ellipse x2a2 + y2b2 = 1 (a > b > 0) are F1 and F2 respectively. If there is an intersection p between the straight line with an inclination angle of 30 ° and the ellipse and the PF2 ⊥ X axis, then the eccentricity e of the ellipse is () A. 33B. 32C. 22D. 23

In RT △ pf2f1, ∠ pf1f2 = 30 °, | F1F2 | = 2c, | Pf1 | = 2 | PF2 |, according to the definition of ellipse, | PF2 | = 23a, | Pf1 | = 43a, and | Pf1 | 2 - | PF2 | 2 = | F1F2 | 2, that is, 169a2-49a2 = 4C2, | e = CA = 33