The two focuses of hyperbola x squared / 9 - y squared / 16 = 1 are f1.f2, Point P is on hyperbola. If Pf1 is perpendicular to PF2, what is the distance from point P to X axis The answer in the book is 16 / 3 | Math enthusiast | Mathematical art

The two focuses of hyperbola x squared / 9 - y squared / 16 = 1 are f1.f2, Point P is on hyperbola. If Pf1 is perpendicular to PF2, what is the distance from point P to X axis The answer in the book is 16 / 3

A & sup2; = 9A = 3 let Pf1 = P, PF2 = q be defined by hyperbola | P-Q | = 2A = 6 square P & sup2; - 2pq + Q & sup2; = 36 vertical then P & sup2; + Q & sup2; = F1F2 & sup2; C & sup2; = 9 + 16 = 25C = 5, so F1F2 = 2C = 10, so 2pq = (P & sup2; + Q & sup2;) - 36 = 10 & sup2; - 36 = 64, so triangle pf1f2 area =

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