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Prove that the radical axis of the circl...

Prove that the radical axis of the circles `x^2+y^2+2gx +2fy+c=0` and `x^2+y^2+2g'x + 2f'y+c'=0` is the diameter of the later circle (or the former bisects the circumference of the later ) if 2g'(g-g')+2f'(f-f')=c-c'

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AAKASH SERIES-SYSTEM OF CIRCLES-EXERCISE 2.2
  1. Find the equation of the radical axis of the following circles x^(2)...

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  2. Find the equation of the radical axis of the following circles. x^2+...

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  3. Find the equation of the common chord of the following pair of circles...

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  4. Find the equation of the common chord of the following pair of circles...

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  5. Find the equation of common chord of the following pair of circlers ...

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  6. Find the equation of the common tangent of the following circles at th...

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  7. Find the equation of the common tangent of the following circles at th...

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  8. Show that the circles x^(2)+y^(2)-8x-2y+8=0 and x^(2)+y^(2)-2x+6y+6=0 ...

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  9. If the two circles x^(2)+y^(2)+2gz+2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 t...

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  10. Find the radical centre of the following circles x^2+y^2-4x-6y+5=0 ...

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  11. Find the equation of the circle which cuts the following circles ortho...

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  12. Show that the common chord of the circles x^2+y^2-6x-4y+9=0 and x^2+y^...

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  13. Find the equation of the common chord of the following pair of circles...

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  14. Find the equation and length of the common chord of the following circ...

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  15. Prove that the radical axis of the circles x^2+y^2+2gx +2fy+c=0 and x^...

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  16. Show that the circles x^(2)+y^(2)+2ax+c=0 and x^(2)+y^(2)+2by+c=0 touc...

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  17. Show that the circles x^(2)+y^(2)-2x=0 and x^(2)+y^(2)+6x-6y+2=0 touch...

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  18. Find the equation of the circle which cuts the following circles ortho...

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  19. Find the equation of the circle which cuts each of the following circl...

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  20. Find the equation of the circle which cuts each of the following circl...

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