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

The locus of the centre of the circle which passes through the origin and cuts off a length 2b from the line x = c is

Find the equation of a circle through origin which cuts of intercepts -2 and 3 units from the x-axis and Y-axis respectively.

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

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 which passes through the origin and cuts off intercepts 3 unit and 4 unit from x and y-axes respectively. Find the equation of that diameter of the circle which passes through the origin.

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

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 intercept form of a plane with intercepts 2,3 and 4 on the x,y and z-axis respectively.

P is the variable point on the circle with center at C. C 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.

Find the equation of plane with intercepts 2,4 and 4 on the x, y and z -axis respectively.