A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point `P` on the rod, which is 3cm from the end in contact with the x-axis.

A rod PQ of length 16 units moves with its ends P and Q always touching x-axis and y-axis respectively. Determine the equation of the locus of a point K on PQ which is always at a distance of 4 unit from P.

A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the locus of a point, which divides the line into two portions of lenghts a unit and b units, is an ellipse. State the situation when the locus will be a circle.

A rod of length k slides in a vertical plane, its ends touching the coordinate axes. Prove that the locus of the foot of the perpendicular from the origin to the rod is (x^2+y^2)^3=k^2x^2y^2dot

Find the locus of a moving point whose distance from the y-axis is always 3

The ends A and B of a rod AB of length 8 unit slide along the lines y=2 and x=4 respectively. Find the equation to the locus of the mid point of the rod.

Find the equation to the locus of a moving point which is always equidistant from the straight lines 3x-4y-2=0and5x-12y=4 .

A line of length (a+b) unit moves in such a way that its ends are always on two fixed perpendicular striaght lines. Prove that the locus of a point on this line which divides it into of lenghts a unit and b unit is an ellipse.

The end’ points of a rod having length l are moving a long with two straight line which are perpendicular toeach othcr. Find the equation -of the locus of the point which divides the rod are in ratio 2:1.

A straight line segment AB of length 'a' moves with its ends on the axes. Then the locus of the point P which divides the line in the ratio 1:2 is