Let p be a point on the ellipse x ^ 2 / 5 + y ^ 2 / 25 = 1, and F1 and F2 be the two focuses of the ellipse. If Pf1 ⊥ PF2, then the absolute value of the difference between Pf1 and PF2 A.0 B.2√5 C.4√5 D.2√15

The focus of the ellipse x ^ 2 / 5 + y ^ 2 / 25 = 1 is on the Y axis, x ^ 2 / A + y ^ 2 / b = 1, so B ^ 2 = 25, a ^ 2 = 5, C ^ 2 = 20
Let Pf1 + PF2 = 2B = 10, | F1F2 | = 2c, let PF2 = m, then Pf1 = 10-m
Pf1 ^ 2 + PF2 ^ 2 = | F1F2 | ^ 2, that is, m ^ 2 + (10-m) ^ 2 = 80, the solution is M1 = 5 + √ 15, M2 = 5 - √ 15
｜PF2｜=5+√15,｜PF1｜=5-√15,|｜PF2｜-｜PF1｜|=2√15.
So choose D

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