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Conic Section

Short Answer Type

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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Long Answer Type

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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Short Answer Type

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

The given equation of the circle is: $open parentheses straight x plus 3 over 2 close parentheses squared plus open parentheses straight y minus 5 over 2 close parentheses squared equals 289 over 4$
Comparing it with $left parenthesis straight x minus straight h right parenthesis squared plus left parenthesis straight y minus straight k right parenthesis squared equals straight r squared comma space we space get$
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∴ the centre of circle is $left parenthesis straight h comma space straight k right parenthesis space left right arrow space open parentheses negative 3 over 2 comma space 5 over 2 close parentheses space and space the space radius space is space 17 over 2$
The radius of circle is $straight r equals 17 over 2$