A rod of length 2 l slides between two perpendicular lines. Find the locus of its middle-point.

The ends of a rod of length l move on two mutually perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.

An ellipse slides between two perpendicular straight lines. Then identify the locus of its center.

An ellipse slides between two perpendicular straight lines. Then identify the locus of its center.

If the extremities of a line segment of length l moves in two fixed perpendicular straight lines, then the locus of the point which divides this line segment in the ratio 1 : 2 is-

A rod AB of length 15 cm rests in between two co-ordinate axes in such a way that the end point A lies on the x-axis and end point B lies on y-axis. A point P (x, y) is taken on the rod in such a way that AP = 6 cm. Prove that the locus of P is an ellipse.

A stick of length 10 units rests against the floor and a wall of a room. If the stick begins to slide ontfloor then the locus of its middle point is:

Show that the line integral of electric field ntensity between any two points depends only on the position of these points and its independent of the path followed between these points.

If the sum of the distances of a variable point from two perpendicular lines in a plane is 1, then its locus is :

Find the equation of the plane passing through the point (3,-3, 1) and perpendicular to the line joining the points (3, 4, - 1) and (2, - 1,5). Also find the coordinates of the foot of the perpendicular, the equation of the perpendicular line and the length of perpendicular drawn from the origin to the plane.

Find the equations of the straight lines passing through the foot of the perpendicular from the point (2,3) upon the straight line 4x+3y+5=0 and bisecting the angles between the perpendicular and the given straight line.