Straight Lines ...

The pair of straight lines joining the origin to the points of intersection of the circles x² + y² = a² and x² + y² + 2(gx + fy) = 0 is

Statement -1: The combined equation is l₁, l₂ is 2x² + 6xy + y² = 0 and that of m₁, m₂ is 4x² + 18xy + y² = 0. If the angle between l₁, m₂ is α then angle between the lines l₂, m₁ is α.
Statement -2: If the pair of lines l₁ l₂ = 0 and m₁ m₂ = 0, are equally inclined then angle between l₁ and m₂ = angle between l₂ and m₁.

If one of the lines ax² + 2hxy + by² = 0 bisects the angle between the coordinate axes, then which of the following can be true

If 4x² + ay² + 2by = c² represents a pair of perpendicular straight lines then