Prove that the points(7,-9) and (11,3) lie on a circle with centre at the origin. Also find its equation.

The differential equation of circles passing through the points of intersection of unit circle with centre at the origin and the line bisecting the first quadrant, is

Show that the points (5, 5),(6, 4),(- 2, 4) and (7, 1) all lie on a circle. Find its equation, centre and radius.

Prove that the points (2, - 1), (0, 2), (3, 3) and (5,0) are the vertices of a parallelogram. Also find the angle between its diagonals.

Prove that the points (2, -1, 3), (1, 2, -1), (3, 4, 5) and (0, -7, -2) are co-planar. Also find the equation of the plane containing these points.

Show that the points A(1, 0), B(2, -7), C(8, 1) and D(9,-6) all lie on the same circle. Find the equation of this circle, its centre and radius.

Show that the points A(1,2),B(-1,-16) and C(0,-7) lie on the graph of the linear equation y=9x-7 .

Find equation of the line through the point (0, 2) making an angle (2pi)/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Prove that the points (1,- 6), (5, 2), (7, 0) and (- 1,-4) are concyclic. Find the radius of the circle.

Find the equation of the circle, which passes through the points (2, - 3) and (3, - 2) and has its centre on the line 2x-3y = 8.