If the origin is shifted to the point (-2,3), axes remaining parallel to the original, what will be the new coordinates of the point (1,-2).

On shifting the origin to the point (1, -1), the axes remaining parallel to the original axes the equation of a curve becomes : 4x^2 + y^2 + 3x- 4y + 2=0 . Find its original equation.

If the origin is shifted (1, 2, -3) without changing the directions of the axis, then find the new coordinates of the point (0, 4, 5) with respect to new frame.

At what point the origin be shifted, if the coordinates of a point (-1, 8) become (-7, 3) ?

The points at which the two coordinate axes is called the

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

A point on x - axis at a distance x from the origin .

The point at which two coordinate axes meet is called

A point on y axis at a distance y from the origin.

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ne (0, 0) is the circle passing through P with origin as centre.