If `e_(1)` and `e_(2)` represent the eccentricity of the curves `6x^(2) - 9y^(2) = 144` and `9x^(2) - 16y^(2) = 144` respectively . Then `(1)/(e_(1)^(2)) + (1)/(e_(2)^(2))` is equal to

Options

A. 0
B. 1
C. 2
D. 3

Answer

B

Explanation

Given curves are `(x^(2))/(9) - (y^2)/(16) = 1` and `(x^(2))/(16) - (y^(2))/(9) = 1`
`therefore " " e_(1) = sqrt(1 + (16)/(9)) = (5)/(3)`
and `e_(2) = sqrt(1 + (9)/(16)) = (5)/(4)`
Now , `(1)/(e_(1)^(2)) + (1)/(e_(2)^(2)) = (9)/(25) + (16)/(25) = 1`