A variable line through point `P(2,1)` meets the axes at `Aa n dB` . Find the locus of the circumcenter of triangle `O A B` (where `O` is the origin).

A variable line through the point P(2,1) meets the axes at A and B .Find the locus of the centroid of triangle OAB (where O is the origin).

The variable line drawn through the point (1,3) meets the x -axis at A and y -axis at B .If the rectangle OAPB is completed.Where O isthe origin,then locus of ^(-)P' is

The variable line drawn through the point (1,3) meets the x-axis at A and y -axis at B .If the rectangle OAPB is completed.Where O is the origin,then locus of P is

a variable line passes through M (1, 2) and meets the co-ordinate axes at A and B, then locus of mid point of AB, is equal to

A variable line passes through M (1, 2) and meets the co-ordinate axes at A and B, then locus of mid point of AB, is equal to

A variable circle having fixed radius 'a' passes through origin and meets the co-ordinate axes in point A and B. Locus of centroid of triangle OAB where 'O' being the origin, is -

A circle of radius 'r' passes through the origin O and cuts the axes at A and B, Locus of the centroid of triangle OAB is

A variable line y=mx-1 cuts the lines x=2y and y=-2x at points A and B Prove that the locus of the centroid of triangle OAB(O being the origin) is a hyperbola passing through the origin.