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If the circle x^2+y^2+2gx+2fy+c=0 bisect...

If the circle `x^2+y^2+2gx+2fy+c=0` bisects the circumference of the circle `x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0` then prove that `2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '`

A

`2g(g-g')+2f(f-f')=c-c'`

B

`2g(g-g')+2f'(f-f')=c'-c`

C

`2g'(g-g')+2f'(f-f')=c-c'`

D

`2g(g-g')+2f(f-f')=c'-c`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-CIRCLES-Exercise
  1. Find the equation of the circle which cuts the three circles x^2+y^2-3...

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  2. The equation of a circle which passes through (2a, 0) and whose radica...

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  3. If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the cir...

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  4. If the pole of a straight line with respect to the circle x^(2)+y^(2)=...

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  5. Find the equation of the chord of the circle x^2+y^2=9 whose middle po...

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  6. Locus of the mid points of the chords of the circle x^2+y^2=a^2 which ...

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  7. If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2)...

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  8. Equation of circle symmetric to the circle x^(2)+y^(2)+16x -24y +183 =...

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  9. The number of the tangents that can be drawn from (1, 2) to x^(2)+y^(2...

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  10. Equation of the circle through the origin and making intercepts of 3 a...

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  11. If y=2x is a chord of the circle x^2+y^2-10 x=0 , find the equation of...

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  12. The tangent to x^(2)+y^(2)=9 which is parallel to y-axis and does not ...

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  13. The two circles x^(2)+y^(2)-5=0 and x^(2)+y^(2)-2x-4y-15=0

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  14. If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , th...

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  15. The circle x^(2)+y^(2)=4 cuts the circle x^(2)+y^(2)-2x-4=0 at the poi...

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  16. If the circle x^2+y^2+2gx+2fy+c=0 is touched by y=x at P such that O P...

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  17. The number of common tangents of the circles x^(2)+y^(2)+4x+1=0 and x...

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  18. The length of the common chord of the circles x^(2)+y^(2)-2x-1=0 and ...

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  19. If a circle passes through the point (a, b) and cuts the circle x^2 + ...

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  20. If the lines 3x-4y+4=0a d n6x-8y-7=0 are tangents to a circle, then fi...

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