# 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#?

##### 1 Answer

Given equations of pair of straight lines are

and

Obviously the straight lines are passing through orin as suggested by the equations.

Now let

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

(1)

and

(2)

By the condition of the problem these two values of

Hence

This is the required condition.