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

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 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=m x-1 cuts the lines x=2y and y=-2x at points Aa n dB . Prove that the locus of the centroid of triangle O A B(O being the origin) is a hyperbola passing through the origin.

If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at Aa n dB , then the locus of the centroud of triangle O A B is (a) x^2+y^2=(2k)^2 (b) x^2+y^2=(3k)^2 (c) x^2+y^2=(4k)^2 (d) x^2+y^2=(6k)^2

A line from (-1,0) intersects the parabola x^(2)= 4y at A and B. Then the locus of centroid of DeltaOAB is (where O is origin)

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 curve is defined parametrically be equations x=t^2a n dy=t^3 . A variable pair of perpendicular lines through the origin O meet the curve of Pa n dQ . If the locus of the point of intersection of the tangents at Pa n dQ is a y^2=b x-1, then the value of (a+b) is____

A variable plane passes through a fixed point (alpha,beta,gamma) and meets the axes at A ,B ,a n dCdot show that the locus of the point of intersection of the planes through A ,Ba n dC parallel to the coordinate planes is alphax^(-1)+betay^(-1)+gammaz^(-1)=1.

Normal is drawn at one of the extremities of the latus rectum of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 which meets the axes at points Aa n dB . Then find the area of triangle O A B(O being the origin).

A line is drawn perpendicular to line y=5x , meeting the coordinate axes at Aa n dB . If the area of triangle O A B is 10 sq. units, where O is the origin, then the equation of drawn line is (a) 3x-y-9 (b) 5y+x=10 (c) 5y+x=-10 (d) x-4y=10