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Let P be a point on the hyperbola H: x29- y24=1, in the first quadrant such that the area of triangle formed by P and the two foci of H is 2 13. Then, the square of the distance of P from the origin is
(2) 22
a2=9, b2=4 ae= a2+b2= 13: foci S1( 13,0), S2(- 13,0)
[figure]
Area = 12 1S2 12 2 13 =2 13 =2
P( ,2) on H: 29- 44=1 2=18
∴ OP2= 2+ 2=18+4=22
Answer: (2)
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