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11. Find the equation of a circle, the two ends of whose diameter are A(4, –5) and R (–2, –1).

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12. Find the equation of a circle which passes through the points (2, 3) and (–1, 1) and whose centre lies on the straight line x – 3y – 11 = 0.

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13. Find the equation of the circle passing through the points A (5, 7), B (6, 6) and C (2, –2).

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14. Find the equation of the circle with radius 5, whose centre lies on x-axis and passing through the point (2, 3).

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15. Find the centre and radii of the following circle:

open parentheses straight x plus 3 over 2 close parentheses squared plus open parentheses straight y minus 5 over 2 close parentheses squared equals 289 over 4

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16. Find the centre and radii of the following circle:

left parenthesis straight x plus 5 right parenthesis squared plus left parenthesis straight y minus 3 right parenthesis squared space equals space 36

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17. Find the centre and radii of the following circle:

straight x squared plus straight y squared equals 49

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18. Find the centre and radii of the following circle:

straight x squared plus straight y squared minus 8 straight x plus 10 straight y minus 12 equals 0

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19. Find the centre and radii of the following circle:

space space 2 straight x squared plus 2 straight y squared minus straight x equals 0

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20. Find the co-ordinates of the centre and the radius of the circle

straight x squared plus straight y squared minus 2 ax space cosθ space minus space 2 ay space sinθ space minus space 8 straight a squared equals 0

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