Given `x/a+y/b=1 and ax + by =1` are two variable lines, 'a' and 'b' being the parameters connected by the relation `a^2 + b^2 = ab`. The locus of the point of intersection has the equation

A variable parabola y^(2) = 4ax, a (where a ne -(1)/(4)) being the parameter, meets the curve y^(2) +x -y- 2 = 0 at two points. The locus of the point of intersecion of tangents at these points is

A variable parabola y^(2) = 4ax, a (where a ne -(1)/(4)) being the parameter, meets the curve y^(2) +x - 2 = 0 at two points. The locus of the point of intersecion of tangents at these points is

A variable parabola y^(2) = 4ax, a (where a ne -(1)/(4)) being the parameter, meets the curve y^(2) +x - 2 = 0 at two points. The locus of the point of intersecion of tangents at these points is

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

Two fixed point A and B are taken on the cordinate axes such that OA = a and OB = b. Two variable points A' and B' are taken on the same axes such that OA'+OB' = OA + OB. Find the locus of the point of intersection of AB' and A'B.

The line x/a+y/b=1 cuts the coordinate axes at a and B a line perpendicular to AB meets the axes in P and Q. The equation of the locus of the point of intersection of the lines AQ and BP is