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If the lengths of tangents drawn to the ...

If the lengths of tangents drawn to the circles
`x^(2) + y^(2) - 8x + 40 = 0`
`5x^(2) + 5y^(2) - 25x + 80 = 0`
`x^(2) + y^(2) - 8x + 16y + 160 = 0`
From the point P are equal, then P is equal to

A

`(8, (15)/(2))`

B

`(-8, (15)/(2))`

C

`(8, (-15)/(2))`

D

`(-8,(-15)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Given circles are, `x^(2) + y^(2) - 8x + 40 = 0`
`x^(2) + y^(2) - 5x + 16 = 0`
`x^(2) + y^(2) - 8x + 16 y + 160 = 0`
Radical axis of equation (2) and equation (3) is 3x - 16y - 144 = 0
Since the lengths of tangents from .P. to given circles are equal P is the radical centre
By solving equation (4) and equation (5)
`:. P = (8, (-15)/(2))`
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SIA PUBLICATION-SYSTEM OF CIRCLE -PROBLEMS
  1. The point at which the circles x^(2)+y^(2)-4x-4y+7=0 and x^(2)+y^(2)-1...

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  2. The length of the common chord of the two circles x^(2) + y^(2) - 4y =...

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  3. The locus of the centre of the circle, which cuts the circle x^(2) + y...

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  4. (a,0) and (b,0) are centres of two circles belonging to a coaxial syst...

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  5. If the circle x^(2) + y^(2) + 4x - 6y + c = 0 bisects the circumferenc...

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  6. A circle passes through the points (3,4) and cuts the circle x^(2) + y...

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  7. The equation to the line joining the centres of the circles belongin...

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  8. If the circle x^(2) + y^(2) + 8x - 4y + c = 0 touches the circle x^...

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  9. The point of contact of the circle x^(2)+y^(2)+2x+2y+1=0 and x^(2)+y^(...

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  10. The equation of the radical axis of the pair of circles 7x^(2) + 7y^(...

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  11. If the lengths of tangents drawn to the circles x^(2) + y^(2) - 8x +...

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  12. If the circle x^(2) + y^(2) + 2x + 3y + 1 = 0 cuts another circle x^(2...

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  13. The point (3,-4) lies on both the circles x^(2) + y^(2) - 2x + 8y + 1...

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  14. The equation of the circle which passes the origin and cuts orthogonal...

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  15. The condition for the coaxial system x^(2) + y^(2) + 2 lambda x + c ...

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  16. The equation of the circle whose diameter is the common chord of the c...

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  17. If the circle x^(2) + y^(2) + 6x - 2y + k = 0 bisects the circumferen...

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  18. The limiting points of the coxail system containing the two circules ...

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  19. The radical axis of circles x^(2) + y^(2) + 5x + 4y - 5 = 0 and x^...

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  20. If the polar of a point on the circle x^(2) + y^(2) = p^(2) with respe...

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