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Let the equation for pair of lines is  " a x² + 2 h x y + b y² = 0 "  .

Let m₁ and m₂ are the slopes of two lines respectively.

Then we have

m₁ + m₂ = - (2h) / b ....................(1)

m₁ m₂ = a/b  .....................(2)

If one of the line is bisecitng the angle between positive direction of axes ,

then slope of this line m₁ = 1 .

Hence , from eqn.(2) , we get ,  m₂ = a/b

By substituting m₁ = 1  and m₂ = ( a / b ) in eqn.(1) , we get

1+ (a/b) = - (2h) / b

From above expression, we get , a+ b = -(2h)