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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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ARIHANT MATHS-CIRCLE -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x+y)=f(x).f(y) for all x and y, f(1) =2 and alpha(n)=f(n),n""inN,...

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  2. Find the derivative of (a/x^4 - b/x^2 + cosx)

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  3. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

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  4. A circle touches the x-axis and also touches the circle with center (0...

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  5. Find the derivative of (4x - 2)

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  6. Let ABCD be a square of side length 2 units. C2 is the circle through ...

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  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  8. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  9. If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of ...

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  10. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

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  11. Find the derivative of (ax + b)^n

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  12. Consider a family of circles which are passing through the point (-1,1...

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  13. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  14. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  15. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  16. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

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  17. The point diametrically opposite to the point P(1, 0) on the circle x^...

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