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Q.

Which of the following pairs may represent the eccentricities of two conjugate hyperbolas, for all α∈(0,π/2)?

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a

sin⁡θ,cos⁡θ

b

tan⁡θ,cot⁡θ

c

sec⁡θ,cosec⁡θ

d

1+sin⁡θ,1+cos⁡θ

answer is C.

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Detailed Solution

If e1 and e2 are the eccentricities of two conjugate hyperbolas,then 1e12+1e22=1Therefore,e1=sec⁡θ and e2=cosec⁡θ.
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