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If the circles x^(2) + y^(2) + 2ax + c^(...

If the circles `x^(2) + y^(2) + 2ax + c^(2) = 0` and `x^(2) + y^(2) + 2by + c^(2) = 0` touch each other, prove that, `(1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2))`.

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CHHAYA PUBLICATION-CIRCLE-Exercise 3 (Long Answer Type Questions)
  1. Find the equation of the circle which touches the x-axis at a distance...

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  2. Show that the circles x^(2) + y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(...

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  3. Prove that the circles x^(2) + y^(2) + 4x - 10y - 20 = 0 and x^(2) + y...

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  4. If the circles x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by...

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  5. Prove that the circles x^(2) + y^(2) - 2x - 4y - 12 = 0 and 3x^(2) + 3...

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  6. Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordi...

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  7. A circle through the common points of the circles x^(2) + y^(2) - 2x ...

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  8. The circle x^(2) + y^(2) + 2x - 4y - 11 = 0 and the line x-y+1=0 inter...

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  9. Find the equation to the circle described on the common chord of the c...

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  10. Find the equation to the locus of mid-points of chords drawn through t...

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  11. A circle passes through the origin O and intersects the coordinate axe...

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

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  13. Find the area of the equilateral triangle inscribed in the circle x^(2...

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  14. Find the area of the equilateral triangle inscribed in the circle x^(2...

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  15. Prove analytically that the straight line joining the middle point of ...

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  16. Find the equation of the circle passing through the point (13, 6) and ...

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  17. Show that the length of the common chord of the circles (x-a)^(2) + (y...

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  18. The abscissae of the two points A and B are the roots of the equation ...

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  19. Find the equation of the circle which touches the x-axis at a distance...

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  20. Prove that the circles x^(2) + y^(2) + 4x - 10y - 20 = 0 and x^(2) + y...

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