Show that the points (-3, 2), (2, -3) and (1, 2`sqrt(3)`) lie on the circumference of that circle, whose centre is origin.

The points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for

Show that the points (9, -2), (-5, 12) and (-7, 10) lie on that circle whose centre is the point (1, 4)

Find the equation of a circle whose centre is (2,-3) and radius 5.

Find the equation of a circle whose centre is (2, 3) and radius is 5.

Figure shows two inclined plane mirros M_(1) and M_(2) and an object O . Its image formed in mirrors M_(1) and M_(2) individually and I_(1) and I_(2) respectively. Show that I_(1) and I_(2) and O lie on the circumference of a circle with centre at I . [This result can be extended to show that all the images will also lie on teh same circle. Note that this result is independent of the angle of inclination of mirrros.]. I is the point of intersection fo the mirrors.

Show that the points (3,2,2), (-1,4,2), (0,5,6), (2,1,2) lie on a sphere whose centre is (1,3,4). Find the also its radius.

Show that the points A(0,4,3) , B(-1,-5,-3), C(-2,-2,1) and D(1,1,1) are coplanar. Also find the equation of the plane in which these points lie.

Does the point ( 2,5), (3,5) lie inside, outside or on the circle x^2+y^2=25 ?

Show that the circle x^2+y^2+4x+4y-1=0 bisects the circumference of the circle x^2+y^2+2x-3=0 .

The four point of intersection of the lines ( 2x -y +1) ( x- 2y +3) = 0 with the axes lie on a circle whose center centre is at the point :