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the eccentricity of the hyperbola (x^(2...

the eccentricity of the hyperbola `(x^(2))/(16)-(y^(2))/(25)=1` is

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Verified by Experts

The correct Answer is:
B
Foci of hyperbola are `(+- sqrt(41),0)`
`:. 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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