[" 8.A is a variable point on x-axis and B(0,b) is a fixied point.A equilateral triangle ABC is completed with "],[" vertex "C" away trom origin.If the locus of the point "C" is "ax+beta y=b" ,then "],[alpha^(2)+beta^(2)is]

On two mutually perpendicular lines,two points A and B are taken such that A is a variable point and B is a fixed point.A equilateral triangle ABC is completed.If the locus of the point C is alpha x+beta y=b, then alpha^(2)+beta^(2) is

A variable line passing through a fixed point (alpha,beta) intersects the coordinate axes at A and B. If O is the origin, then the locus of the centroid of the DeltaOAB is

A variable line whose slope is -2 cuts x and y-axes respectively at points A and C. If Rhombus ABCD is completed such that the vertex B lies on the line y =x then the locus of the vertex D is

A variable line intersects the co-ordinate axes at A and B and passes through a fixed point (a,b). then the locus of the vertex C of the rectangle OACB where O is the origin is

A variable line intersects the co-ordinate axes at A and B and passes through a fixed point (a, b) .then the locus of the vertex C of the rectangle OACB where O is the origin is

A variable line intersects the co-ordinate axes at A and B and passes through a fixed point (a, b), then the locus of the vertex C of the rectangle OACB where O is the origin is :

The base BC of an equilateral triangle ABC, lies on y-axis. The coordinates of point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B.

If alpha , beta are the roots of ax^2+bx +c=0 then (a alpha + b)^(-2)+( a beta + b)^(-2) =