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If f(x+y)=f(x).f(y) for all x and y, f(1...

If f(x+y)=f(x).f(y) for all x and y, f(1) =2 and `alpha_(n)=f(n),n""inN`, then the equation of the circle having `(alpha_(1),alpha_(2))and(alpha_(3),alpha_(4))` as the ends of its one diameter is

A

`(x-2)(x-8)+(y-4)(x-16)=0`

B

`(x-4)(x-8)+(y-2)(x-16)=0`

C

`(x-2)(x-16)+(y-4)(y-8)=0`

D

`(x-6)(x-8)+(y-5)(y-6)=0`

Text Solution

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The correct Answer is:
`(x-2)(x-8)+(y-4)(x-16)=0`
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