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Problem 5

If \(f(x+y)=f(x) f(y)\) for all \(x\) and \(y, f(1)=2\) and $\alpha_{n}=f(n), n \in N\( then the equation of the circle having \)\left(\alpha_{1}, \alpha_{2}\right)\( and \)\left(\alpha_{3}, \alpha_{4}\right)$ 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) \((x-2)(x-16)+(y-4)(y-8)=0\) (d) \((x-6)(x-8)+(y-5)(y-6)=0\)

Expert verified

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

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Chapter 1

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