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.

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.

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

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

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

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

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

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). x y=4 (b) x y=1/4 x y=1 (d) none of these

A variable circle passes through the fixed point (2, 0) and touches y-axis Then, the locus of its centre, is

A variable circle passes through the fixed point (2, 0) and touches y-axis Then, the locus of its centre, is

The circle x^2+y^2-4x-4y+4=0 is inscribed in a variable triangle O A Bdot Sides O A and O B lie along the x- and y-axis, respectively, where O is the origin. Find the locus of the midpoint of side A Bdot