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 gradient of one of the lines given by  is twice that of the other, then

The equation x³ + y³ = 0 represents

One bisector of the angle between the lines given by

 . The equation of the other bisector is

The equation  represents two mutually perpendicular lines if

The product of the perpendiculars drawn from the point (1, 2) to be the pair of lines x² + 4xy + y² = 0 is

The three lines whose combined equation is y³ – 4x²y = 0 form a triangle which is

The angle between the pair of lines whose equation is

If two of the straight lines represented by   are at right angles, then,

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

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