A variable line through the point `P(2,1)` meets the axes at a an d b . Find the locus of the centroid of triangle `O A B` (where `O` is the origin).

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

If a circle of constant radius 3K passes through the origin and meets the axes at A&B.the locus of the centroid of triangleOAB is

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is-

A line is drawn through the point ( 1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is

A variable line is at constant distance p from the origin and meets the co-ordinate axes in A, B. Show that the locus of the centroid of the triangleOAB is x^(-2)+y^(-2)=9p^(-2)

A curve is defined parametrically by the the equation x=t^(2) and y=t^(3). A variable pair of peerpendicular lines through the origin O meet the curve at P and Q. If the locus of the point of intersectin of the tangents at P and Q is ay^(2)=bx-1, then the value of (a+b) is "______."

A variable plane passes through a fixed point (a,b,c) and meets the axes at A ,B ,a n dCdot The locus of the point commom to the planes through A ,Ba n dC parallel to the coordinate planes is

A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

A variable line passes through a fixed point (x_(1),y_(1)) and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes)