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.

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of the point which divides this line into portions of length aa n db is (a) an ellipse (b) parabola (c) straight line (d) none of these

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.

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

A line segment of length (a+b) units moves on a plane in such a way that its end points always lie on the coordinates axes. Suppose that P is a point on the line segment it in the ratio a:b. Prove that the locus of P is an ellipse.

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 .

A rod of length l slides with its ends on two perpendicular lines. Find the locus of its midpoint.

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 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.

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (!=1) . Then, identify the locus of the point.

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.