A rod of length a unit slides on the x-axis and another rod of length b unit slides on the y-axis in such a way that the four extremities of the rod are concylic. Show that the locus of the centre of the circle is `4(x^(2)-y^(2))=a^(2)-b^(2)`.

Two rods of lengths a and b slide along the x- and y-axis , respectively, in such a manner that their ends are concyclic. Find the locus of the center of the circle passing through the endpoints.

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.

A circle is drawn to cut a chord of length 2a unit along x-axis and to touch the y-axis. Then the locus of the centre of the circle is-

A circel cuts intercepts of lenghts 2a and 2b from the x-axis and the y-axis respectively. Then the equation to the locus of the centre of the circel is-

A circle touches the x-axis and also touches the circle with centre (0,3) and radius2. The locus of the centre of the circle is

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.

If the intercepts of the variable circle on the x- and y-axis are 2 units and 4 units, respectively, then find the locus of the center of the variable circle.

The circle A and B of a line segment of constant length c unit slides upon the fixex rectangular axes OX and OY. If P be a point on the plane such that OAPB is a rectangle, then show that locus of the foot of the perpendicular drawn from P to AB is x^(2//3)+ y^(2//3)=c^(2//3) .

A variable circle passes through the point A(a, b) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x-a)^2 = 4by

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