Find the locus of the center of the circle which cuts off intercepts of lengths `2aa n d2b` from the x-and the y-axis, respectively.

Prove that the locus of the center of a circle, which intercepts a chord of given length 2a on the axis of x and passes through a given point on the axis of y distant b from the origin, is a parabola.

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and -6, respectively.

Find the equation of the circle with center at (3,-1) and which cuts off an intercept of length 6 from the line 2x-5y+18=0

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 locus of centre of a circle which passes through the origin and cuts off a length of 4 units on the line x =3 is

Find the locus of center of circle of radius 2 units, if intercept cut on the x-axis is twice of intercept cut on the y-axis by the circle.

The locus of the center of a circle which cuts orthogonally the parabola y^2=4x at (1,2) is a curve

Find the locus of the centres of the circle which cut the circles x^2+y^2+4x-6y+9=0 and x^2+y^2-5x+4y-2=0 orthogonally

Find the middle point of the chord of the circle x^2+y^2=25 intercepted on the line x-2y=2

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.