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Conic Section

Short Answer Type

31. Find the equation of a circle which has its centre at point (2, 4) and which passes dirough the mid -point of the line segment joining the points (3, – 1) and (– 3, 5).

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32. Find the equation of circle which has a radius of 5 units and the centre at the point of intersection of the lines 2x – y + 4 = 0 and x + 3y – 5 = 0

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33.

Find the equation of circle which has 3x - 2y - 4 = 0 and 2x + y - 5 = 0 as two of its diameters and a radius of $2 square root of 2.$

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34. Find the equation of a circle whose centre is (2, - 3) and has an area of 38.5 sq. units.

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35. Find the equation of a circle whose centre is at point (– 3, 2) and which touches the straight line 5x + 12y + 30 = 0.

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36. Find the equation of circle which passes through the points (5, 5) and (– 2, 4) has its centre on the straight line 2x – y = 3.

Solution not provided.
Ans. $straight x squared plus straight y squared minus 4 straight x minus 2 straight y minus 20 equals 0$

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37. Find the equation of circle passing through the points (4, 1) and (6, 5) and whose centre lies on the straight line 4x + y = 16.

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38. Find the equation of circle passing through the origin and points (4, 0) and (0, 5).

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39. Find the equation of the circle passing through the origin and cutting of intercepts 2a and 2b on the co-ordinate axes.

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40. Find the equation of a circle whose centre lies on the y-axis, which has a radius of 5 units and passes through the point (3, 2).

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