The Equation  represents Three Straight Lines Passing Through The Origin Such That

The orthocentre of the triangle formed by the pair of lines  and the line x + y + 1 = 0 is 

If the distance of a point (x₁, y₁) from each of the two straight lines, which pass through the origin of coordinates, is δ, then the two lines are given by  

The equation of two straight lines through the point (x₁, y₁) and perpendicular to the lines given by 

The equation of the straight lines through the point (x₁, y₁) and parallel to the lines given by 

The triangle formed by the lines whose combined equation is  

The combined equation of the pair of lines through the point (1, 0) and perpendicular to the lines represented by 

The equation x³ + ax²y + bxy² + y³ = 0 represents three straight lines, two of which are perpendicular, then the equation of the third line is  

The combined equation of the lines L₁ and L₂ is 2x² + 6xy + y² = 0 and that of the lines L₃ and L₄ is 4x² + 18xy + y² = 0. If the angle between L₁and L₄ be α, then the angle between L₂ and L₃ will be   

The lines represented by  and the lines represented by  are equally inclined then

If the equation  represents two pairs of perpendicular lines, then