Find the condition that one of the straight lines given by the equation #ax^2+2hxy+by^2=0# may coincide with one of those given by the equation #a_1x^2+2h_1xy+b_1y^2#?
Given equations of pair of straight lines are
Obviously the straight lines are passing through orin as suggested by the equations.
So by (1) and (3) we get
Similarly by (2) and (3) we will get
By cross multiplication of (4) and (5) we get
Hence we get two values of
By the condition of the problem these two values of
This is the required condition.