Find the equation to the locus of a point whose distance from the X-axis is double its distance from the Y-axis.

Find the equation to the locus of a point which moves such that the sum of the squares of its distances from the points A(1, 0) and B(-1, 0) is 10.

Find the equation to the locus of a point which moves in a plane such that its distance from the point (1, 2) is equal to its distance from the Y-axis.

Find the equation to the locus of a point which is equidistant from the points (1, 1) and (-1, -1).

Find the points on the X- axis whose distance from the point (2, -3, 4) are 13 units.

Find the equation of the parabola whose vertex is at the origin, axis is along the X-axis and the length of the latus rectum is 4 units.

Find the coordinates of the point in the octant OXYZ whose distances from the axes are 4 sqrt5 , 5 sqrt3 and 5 respectively.

Two lines parallel to the y-axis and at a distance of2 units from the x-axis are taken. Another two lines parallel to the x-axis and at a distance of 3 units from the y-axis are also taken. Find the distance of the angular points of the rectangle, formed by the four intersecting line segments, from the origin.

Find the equation of an cllipse in its standard form with major axis X-axis and minor axis along Y-axis when the distance between the foci is 2 units and that between the directrices is 4 units.

Find the equation of line in space parallel to X-axis and passing through the origin

Find the distance of the point (3,4,-5) from Z-axis.