Show that the tangent of an angle between the lines xa+yb=1 and xa−yb=1 is 2aba2−b2
Let the line xa+yb=1 be AB and the line xa−yb=1 be CD.
Equation of AB, bx+ayab=1
Similarly, the equation of CD, bx−ayab=1
The tangent of angle between the lines AB and CD is
tan θ=∣∣m1−m21+m1m2∣∣=∣∣ ∣∣−ba−ba1+(−ba)(ba)∣∣ ∣∣
The tangent of the angle between the lines =2aba2−b2