If for all and

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If f(x+y)=f(x)⋅f(y)f(x+y) = f(x) \cdot f(y) for all xx and yy , f(1)=2f(1) = 2 and αn=f(n),n∈N\alpha_n = f(n), n \in N , then the equation of the circle having (α1,α2)(\alpha_1, \alpha_2) and (α3,α4)(\alpha_3, \alpha_4) as the ends of its one diameter is (1) (x−2)(x−8)+(y−4)(y−16)=0(x-2)(x-8) + (y-4)(y-16) = 0 (2) (x−4)(x−8)+(y−2)(y−16)=0(x-4)(x-8) + (y-2)(y-16) = 0 (3) (x−2)(x−16)+(y−4)(y−8)=0(x-2)(x-16) + (y-4)(y-8) = 0 (4) (x−6)(x−8)+(y−5)(y−6)=0(x-6)(x-8) + (y-5)(y-6) = 0

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