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Prove that the circles x^(2)+y^(2)+2ax+a...

Prove that the circles `x^(2)+y^(2)+2ax+ay-3a^(2)=0andx^(2)+y^(2)-8ax-6ay+7a^(2)=0` touch each other.

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Prove that the circle x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0 touch each other if (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) .

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NAGEEN PRAKASHAN ENGLISH-CONIC SECTION-Exercise 11A
  1. Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-4y-11...

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  2. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

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  3. Prove that the circles x^(2)+y^(2)+2ax+ay-3a^(2)=0andx^(2)+y^(2)-8ax-6...

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  4. If the circles x^(2)+y^(2)+2ax+c=0andx^(2)+y^(2)+2by+c=0 touch each o...

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  5. (i) Find the point at which the circle x^(2)+y^(2)-5x+2y+6=0, meets th...

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  6. (i) Find the equation of a circle concentric with the circle x^(2)+y^(...

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  7. Find the distance between the centres of the circles x^(2)+y^(2)+8x+10...

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  8. Find the equations of the circles the end points of whose diameter are...

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  9. The end points of a diameter of a circle are (1,-1) and (3,5). Find th...

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  10. Find the equation of a circle passes through the origin and cuts 'a' i...

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  11. Show that equations of a circle with end points of diameter (x(1),y(1)...

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  12. Find the equation of a circle whose centre is (2,-1) and touches the l...

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  13. Find the equation of circle with Centre C (1,- 3) and tangent to 2 x ...

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  14. Find the equation of circle passing through the point (2,1), (1,2) and...

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  15. Find the equation of the circle which passes through the points (3,-2)...

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  16. Find the equation of the circle passing through the points (1,-2)a ...

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  17. Find the equation of circle passing through the points (0,5) and (6,1)...

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  18. Find the equation of circle passing through the points (1,-2) and (3,-...

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  19. Find the equation of a circle circumscribing the triangle whose sides ...

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  20. Find the equation of a circle passing through the points (-1,5) and (-...

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