Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively. If P is on hyperbola and Pf1 vector * PF2 vector = 0, then | Pf1 vector + PF2 vector | =? The answer is 2 root 10. But I can't work it out

Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively. If P is on hyperbola and Pf1 vector * PF2 vector = 0, then | Pf1 vector + PF2 vector | =? The answer is 2 root 10. But I can't work it out

PF1⊥PF2
Let F 2 be f 2 h ∥ P F 1 and F 1 h ∥ P F 2, then pH is F 1 + P F 2
This is a rectangle, so the diagonals are equal
|PF1+PF2|= |PF1-PF2|=|F1F2|=2c
Hyperbola C = radical (1 + 9) = radical 10
|Pf1 + PF2 | = 2 root 10