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If P is any point common to the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 and the circle having line segment joining its foci as diameter then sum of focal distances of point P is |
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Answer» `6sqrt(2)` `:. P` LIES on the circle `x^(2) + y^(2) = 41` Any point on hyperbola is `(4 sec theta, 5 tan theta)` `rArr 16 sec^(2) theta + 25 tan^(2) theta = 41` `rArr tan theta = (5)/(sqrt(41))` and `sec theta = sqrt((66)/(41))` `:. PF_(1) + PF_(2) = e (4 sec theta -(a)/(e)) +e (4 sec theta +(a)/(e))` `= 8 esec theta = 2 sqrt(66)` |
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