1.Find the equation of the circles with

(i)center (ii)center

(iii)center (iv)center and radius

2.Find the equation of the circle passing through and cutting intercepts on the positive side of axes respectively .

3.Find the equation of the circle having radius 5 and passing through two points on x-axis at distance 4 from the origin .

4.Find the equation of the circle passing through the point and center at the point of intersection of the lines

5.If the equation of the two diameters of a circle are and the radius is 10, find the equation of the circle .

6.Find the equation of the circle of radius 5 whose center lies on y-axis and which passes through the point

7.Find the equation of the circle which passes theough the points and whose center lies on the line

8.Find the equation of the circle which touches the axis of at a distance 4 from the origin and cuts off an intercept of length 6 on the axis of

9.Find the equation of the circle whose center is and which passes through the point

10.If the equation of the two diameters of a circle are and the radius of the circle is 10, find the equation of the circle .

11.The line is tangent to the circle at the point and the center of the circles is on the line Find the equation of the circle .

12.Find the equation of the circle which passes through the origin and cuts off intercepts 6 and 8 from the positive parts of axes respectively .

13.Find the equation of the circle which touches

(i)y-axis and has center at (ii)y-axis at the origin and has radius 4 .

14.Find the equation of the circle which touches the lines and lies in the first quadrant .

15.Find the equation of the circle having radius 2 and touching both axes .

16.Find the equation of the circle whose center is and which touches the line

17.Find the equation of the circle passing through two points on y-axis at distances 3 from the origin and having radius 5 .

18.Find the equation of the circle of radius 5 whose center lies on x-axis and passes through the point

19.A circle has radius 3 units and its center lies on the line Find the equation of the circle if it

passes through

20.Find the equation of the circle passing through the points and whose center lies on the line

21.One of the diameters of the circle circumscribing the rectangle is . If are the

points respectively , find the area of the rectangle and equation of the circle .

22.Find the equation of the circles which touch the axes and whose center lies on the line

23.Find the equation to the circles touching y-axis at and making an intercept of 8 units on the x-axis .

24.Find the equation of the circle which touches the axis of at a distance 3 from the origin and cuts an intercepts of length 6 on the axis of .

25.A circle of radius 5 units touches the coordinate axes in the first quadrant . If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in the new position .

26.Find the center and radius of the circle

27.Find the center and radius of the circle

28.Find the center and radius of the circle .

29.Prove that the radii of the circles are in A.P. .

30.Find the coordinates of the middle point of the chord which the circle cuts off on the line

31.(a)Examine whether the following equations represent a circle or not .

(b)Examine whether the following equations represent a circle or not .

(c)Examine whether the following equations represent a circle, a point or no circle .

(d)Determine whether the following equations represent a circle or not .

32.Prove that the centers of the circles are collinear .

33.Find the equation of the circle which is concentric with the circle and the doucle of its area .

34.Find the equation of the circle concentric with the circle and having radius double of its radius .

35.The line is tangent to a circle at the point and center of the circle is on the line Find the equation of the circle .

36.The line is tangent at the point and the line is tangent at the point

to a circle . Find the equation of the circle .

37.Find the equation of the circle circumscribing the quadrilateral formed by the straight line

38.Find the area of an equilateral triangle inscribed in the circle .

39.Find the equation of the circle passing through the vertices of the triangle whose sides are

40.Find the equation of the circle passing through the point and the points where the straight line meets the axes of coordinates .

41.Show that the points all lie on a circle . Find its equation, center and radius .

42.Find the equation of the circle which passes through the center of the circle and

is concentric with the circle

43.Find the equations to the circles touching y-axis at and making intercept of 8 units on the x-axis .

44.Find the equations of the circles passing through the following three points

(i) (ii) .

45. Find the equations of the circle when the end points of a diameter are and . Also find its center and radius.

46. Find the equations of the circle whose diameter is the line segment joining the points Find also the intercept made by it on y-axis .

47. The abscissa of two points are the roots of the equation and their ordinates

are the roots of the equation Find the equation and the radius of the circle with as diameter.

48. Find the equation of the circle passing through the point and the points where the straight line meets the axes of coordinates.

49.Find the equation of the circle whose diameter is the portion of the line , intercepted by the lines

50.The sides of a square are Find the equation of the circle on the diagonal of the square as its diameter .

51.Find the equation of the circle drawn on the intercept between the axes made by the line as a diameter .

52.Show that the equation of the circle passing through the origin and cutting intercepts on the

coordinate axes is

53.If be end of a diameter of the circle find the coordinates of the other end of the diameter .

54.Th sides of a square Find the equation of a circle drawn on the diagonal of the square as its diameter .

55.Find the equation of the circle circumscribing the rectangle whose sides are are

56.Find the parametric equations of the following circles

(a) (b)

(c) (d) .

57.Find the equation of the circle in parametric form whose diameters are and area is 154 .

58.Find the Cartesian equation of the following curves whose parametric equation .

59. Find the Cartesian equation of the following curves whose parametric equation .

60. Find the Cartesian equation of the following curves whose parametric equation .

61. Find the Cartesian equation of the following curves whose parametric equation .

62.Show that

63.Show that the point where lies on a circle for all values of .

64.Prove that

65.Show that the point where lies on a circle for all values of .

66.Show that the point where lies on a circle for all values of .

67.Determine the number of points of intersection of the circle with each of the following lines

(i) (ii) .

68.Find the points in which the line cuts the circle Also find the length of the chord intercepted .

69.Find the points of intersection of the circle and the line Also find the length of the chord intercepted .

70.If is a chord of the circle find the equation of the circle with this chord as diameter . Hnece find the length of the chord intercepted .

71.Find the length of intercepted made by the circle on the x-axes .

72.Prove that the line a touches the circle Also find the point of contact .

73.Find the condition that the line may touch the circle

74.If the circle touches the line find the values of .

75.Find the equation to the circle which is concentric with and touches the line

76.Find the equations of the tangents to the circle which are parallel to the line

77.Find the equations of the tangents to the circle which are perpendicular to the line

78.Find the equations of the tangents to the circles which make an angle of with the positive direction of x-axis .

79.Find the equation of the tangents to the circles drawn from the point

80.Find the equations of the tangents to the circles through the origin .

81.Find the equations of the tangents drawn from the point to the circle

82.Find the equations of the circle which touches the line passes through origin and the point where

the curve meets the x-axis .

83.Find the equations of the circles which have radius and touch the line at

84.Find the equations of the circles satisfying the given conditions:-

Touches the line at and tangent to

85.If the line touches the circle prove that the point lies on the circle

86.Prove that the line touches the circle Also find the point of contact .

87.Find the equations of the tangents to the circle which are perpendicular to the line .

88.The line is a tangent to a circle at the point and its center is on the line Find the equation of the circle .

89.Find the equation of the circle having radius 5 and touching the line at the point

90.Find the equation of the circle passing through the point and touching the line at

the point

91.Prove that the circle lies entirely inside the circle

92.Prove that the circles .

93.Show that the circles .

94.Prove that the circles touch one another and find the equation of the tangent at their point of contact .

95.Show that the circles touch each other . Do these circles touch externally or internally . Also find their point of contact .

96.Find the equation of the circle whose radius is 3 and which touches the circle

internally at the point

97.A circle of radius 2 lies in the first quadrant and touches both the axes of co-ordinates . Find the equation

of the circle with center at and touching the above circle externally . Also find the equation of the common tangent at the point where the two circles touch each other .

98.Find the equation of the family of circles passing through the points

99.Find the equation of the circle which passes through the origin and the point of intersection of the circles

.

100.Find the equation of the circle which passes through the point and through the points of

intersection of the circles .

101.Find the equation of the circle passing through the point and through the points of intersection of

the circle and the line .

102.Find the equation of the circle which passes through the intersection of the circles

and and has its center on the line .

103.Find the equation of the circle whose diameter is the chord of the circle .

104.If be the equation of a chord of a circle prove that the equation of the circle

of which this chord is diameter is .

105.Find the equation of the smallest circle passing through the common points of the two circles

106.Find the equations of the circle which touch and pass through the points of intersection of

the line and the circle

107.If the line cuts the circle in , then show that the circle

whose diameter is is .

108.Find the equation of the circle pass through the points of intersection of the circles

and radius is 3 .

109.Find the equation of the circle passes through the points of intersection of

and touches the line

110.Find the values of for which the line does not intersect the circle

111.Find the points on the circle whose distance from the line is units .

112.A circle cuts the axis of at the point and it circumscribes an equilateral triangle with as one of its sides, where is the origin . Find the value of a and the vertices of the equilateral triangle .

113.Find the equations of the circle passing through the point and touching the lines

114.Prove that the circles by touch if

115.Find the nearest point and the farthest point on the circle from the point

116.The circle does not intersect or touch either axis and the point is inside the circle .Calculate the range of possible values of

117.Find the equation of a circle touching the line at the point and passing through the

point

118.Find the equation of the circle with center on the line and touching the lines .

119.Find the equations of circles with radius 3 and which touch the circle at the

point

120.If the two circles interest in two distinct points, then prove that c

121.Show that the circles passes through the point for all values of If varies, find

(i)the equation of the locus of the center of the circle

(ii)the value of for which the line is a tangent top the circle .