What are the coordinate of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and three edge passing through the origin coincides with the positive direction of the axis `theta` through the origin.

Find the equation of a line through the origin which makes an angle of 45^0 with the positive direction of x-axis.

A square of side a lies above the X- axis and has one vertex at the origin . The side passing through the origin makes an angle pi//6 with the positive direction of X-axis .The equation of its diagonal not passing through the origin is

Circle with centre (-1,2) and passing through origin is

Circle will centre origin and passing through (-1,2) is

Equation of the circle with centre on the y-axis and passing through the origin and (2, 3) is

The direction cosines of the line passing through P(2,3,-1) and the origin are

A square of each side 2, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30^(@) with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is:

Equation of the circle with centre lies on y-axis and passing through the origin and the point (2,3) is

Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with positive direction of X axis is 15o .

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is