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 equaqtion of the circle having `(alpha_(1),alpha_(2))and(alpha_(3),alpha_(4))` as the ends of its one diameter is

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

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

If f(x+y) = f(x).f(y) for all x and y. f(1)=2 , and alpha_n = f(n), n epsilon N , then 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) (y-16) = 0 (B) (x-4) (x-8) + (y-2) (y-16) = 0 (C) (x-4) (x-16) + (y-4) (y-8) = 0 (D) none of these

If f(x+y) = f(x).f(y) for all x and y. f(1)=2 , and alpha_n = f(n), n epsilon N , then 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) (y-16) = 0 (B) (x-4) (x-8) + (y-2) (y-16) = 0 (C) (x-4) (x-16) + (y-4) (y-8) = 0 (D) none of these

If f(x+y)=f(x)f(y) for all x and y,f(1)=2 and a_(n)=f(n),n in N, then the equation of the circle having (a_(1),a_(2)) and (a_(3),a_(4)) as the ends of its one diameter

If alpha_(1),alpha_(2),alpha_(3)......alpha_(n) are roots of the equation f(x)=0 then (-alpha_(1),-alpha_(2),-alpha_(3),......alpha_(n)) are the roots of

If f(x) = x^2 - 3x + 1 and f (2 alpha) = 2 x f(alpha) =

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is