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.

If one end of the diameter is (1, 1) and the other end lies on the line x+y=3 , then find the locus of the center of the circle.

If the coordinates of a variable point P are (acostheta,bsintheta), where theta is a variable quantity, then find the locus of Pdot

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.

A circle touches the y axis at (0,2) and its x intercept equal to 3 units, then the equation of the circle 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

When a particle moving in a vertical circle the variable is are

A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. Then find the radius of the circle.

The point on a circle nearest to the point P(2,1) is at a distance of 4 units and the farthest point is (6, 5). Then find the equation of the circle.