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 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.

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.

The end points P and Q of a rod PQ having length 8 unit slide along the lines y = 2 and x = 4 respectively. Find the equation of the locus of the mid point of the rod.

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.

Find the equation to the locus of a moving point which is always equidistant from the points (3 , 4 , -5) and ( - 2, 1 , 4)

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 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 line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has equation.

Taking major and minor axes as x and y - axes respectively , find the equation of the ellipse whose distance between the foci is 4sqrt(3) unit and minor axis is of length 4 unit .