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Prove that the centres of the circles `x^(2) + y^(2) - 10x + 9 = 0, x^(2) + y^(2) - 6x + 2y + 1 = 0` and `x^(2) + y^(2) - 18x - 4y + 21 = 0` lie on a line, find the equation of the line on which they lie.

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The correct Answer is:
x - 2y = 5
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CHHAYA PUBLICATION-CIRCLE-Exercise 3 (Short Answer Type Questions)
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  2. Show that the points (2, 0), (5, -3), (2, -6) and (-1, -3) are concycl...

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  3. Prove that the centres of the circles x^(2) + y^(2) - 10x + 9 = 0, x^(...

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  4. Show that the centres of the following circles lie on a line and their...

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  5. Find the equation of the circle which passes through the origin and cu...

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  6. Find the equation of the circle circumscribing the triangle formed by ...

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  7. The extremities of a diameter of a circle are the points (4, -2) and (...

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  8. Find the equation of the circle through the points (4, 3) and (-2, 5) ...

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  9. A circle has its centre on the straight line 5x - 2y + 1 = 0 and cuts ...

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  10. The equations of a diameter of a circle is 2x - y + 4 = 0 and it passe...

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  11. A circle passes through the points (-6, 5), (-3, -4) and its radius is...

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  12. 3x + y = 5 and x+y+1 = 0 are two diameters to the circle which passes ...

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  13. A circle passes through the points (-3, 4), (1, 0) and its centre lies...

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  14. Find the equation of the circle which has its centre on the line y = 2...

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  15. Find the equation to the circle which touches the y-axis at the origin...

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  16. A circle touches the x-axis at (3, 0) and its radius is twice the radi...

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  17. A circle touches y-axis at (0, 5) and whose centre lies on the line 2x...

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  18. Find the equation of a circle which passes through the point (4, 2) an...

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  19. Two cirles of radii 2 and 10 units respectively pass through (2, 4) an...

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  20. Prove that the point (-1, -2) lies on the circle x^(2) + y^(2) - x y -...

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