If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec α - y sec α = k cot 2 α and x sin α + y cos α = k sin 2 α respectively, then k 2 is equal to :

Step-by-step solution

L 1 : x cosec α - y sec α = k cot 2 α x sin α - y cos α = k cos 2 α sin 2 α x cos α - y sin α sin α   cos α = k cos 2 α 2   sin α   cos   α ⇒ x cos α - y sin α = k 2 cos 2 α We know that Perpendicular distance from a point x 1 ,   y 1   to a x   + b y   +   c   =   0 is a x 1   +   b y 1   +   c a 2 + b 2 Perpendicular distance from ( 0 , 0 ) is p = 0