A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. The point O divides the segment PQ in the ratio

A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P(a, 0) and the Y-axis at Q(0, b). If AQ and BP intersect at R, the locus of R is

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).

A straight line through the point (3, $$-$$2) is inclined at an angle 60$$^\circ$$ to the line $$\sqrt 3 x + y = 1$$. If it intersects the X-axis, then its equation will be