If The Coordinates Axes Are The Bisectors Of The Angles Between The Pair Of Lines ax2 + 2hxy + by2 = 0, Then

The combined equation of the images of the pair of lines given by ax² + 2hxy + by² = 0 in the line mirror y = 0, is   

The difference of the tangents of the angles which the lines  make with X-axis, is 

The product of perpendiculars let fall from the point (x₁, y₁) upon the lines represented by ax² + 2hxy + by², is

The angle between the The Pair of Straight Lines

The pair of lines represented by 3ax² + 5xy + (a² – 2)y² = 0 are perpendicular to each other for 

The angle between the pair of lines represented by 2x² – 7xy + 3y² = 0, is   

The angle between the lines represented by , is

If the angle θ is acute, then the acute angle between 

If θ is the acute angle between the lines given by x² – 2pxy + y² = 0, then,

 bisect angles between each other, then