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

A variable circle cuts x -y axes so that intercepts are of given lengthk _(1) and k_(2). Find the locus of the centre of circle

Variable circles are drawn touching two fixed circles externally then locus of centre of variable circle is

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.

P is the variable point on the circle with center at C.CA and CB are perpendiculars from C on the x - and the y-axis,respectively. Show that the locus of the centroid of triangle PAB is a circle with center at the centroid of triangle CAB and radius equal to the one- third of the radius of the given circle.

A circle touches the x -axis and also touches the circle with center (0,3) and radius 2. The locus of the center

The circle x^(2)+y^(2)-4x-4y+4=0 is inscribed in a variable triangle OAB. sides OA and OB lie along the x -and y -axis, respectively,where O is the origin.Find the locus of the midpoint of side AB.

Circle S_(1) is centered at (0,3) with radius 1. Circle S_(2) is externally tangent to circle S_(1) and also tangent to x-axis.If the locus of the centre of the variable circle S_(2) can be expressed as y =1+ ( x^(2))/( lambda) . Find lambda

The sum of the intercepts cut off from the coordinate axes bya variable line is 14 units. Find the locus of the point which divides internally the portion of the line intercepted betweenthe coordinate axes in the ratio 3:4.

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8units and 6units on the x and y-axis,respectively.If the eccentricity of all such ellipses is (1)/(2), then find the locus of the focus.