GRADE - X : Circle:Long practice questions + solutions

Q.No. 23 – Co-ordinate geometry (Circle )

A.      Circle:

     1.       A circle of  two diameter of a circle passing through the points (0,2) are       4x – 2y = 5 and 8x + 6y = -5. Find the equation of the circle.                                                                         [2068 S’ ]

2.     2.  Find the equation of the circle passing through the points (2,3) and (5,4) and centre lies on the line 2x + 3y – 7 = 0.                                                                                                                                 [2073 R’]

3.    3.   Find the equation of the circle which touches the X-axis at a point (3,0) and passing through point (1, 2 ).                                                                                                                                                [2064 R’]

4.      On a wheel , there are three points (5,7), (-1,7) and (5,-1) located such that the distance from a fixed points to those points is always equal. Find the coordinates of the fixed point and then derive the equation representing the locus that contains all three points.                            [SEE Model 2076]

5.     5.  If the line x + y = 1 and cuts a circle x² + y² = 1 at two points, find the distance between the two points.                                                [2062 R]

6.      Find the equation of a circle concentric with the x² + y²  - 6x +y = 1 and passing through the points (4,-2 ).                                                                                                                                             [2072R’]

7.     7.  Find the equation of the circle with the centre (-1,2 ) and  it passes through the centre of circle x² + y²  - 6x -10y - 2 = 0.                                                                                                                       [2075 R]