If the bisectors of the angles between the pa | vedclass

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(D) The equation of the pair of angle bisectors for $ax^2 + 2hxy + by^2 = 0$ is given by $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$ ... $(i)$.The second

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Any real number

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(D) The equation of the pair of angle bisectors for $ax^2 + 2hxy + by^2 = 0$ is given by $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$ ... $(i)$.The second equation is $(a + \lambda)x^2 + 2hxy + (b + \lambda)y^2 = 0$.The equation of the pair of angle bisectors for this equation is $\frac{x^2 - y^2}{(a + \lambda) - (b + \lambda)} = \frac{xy}{h}$,which simplifies to $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$ ... $(ii)$.Since equation $(i)$ and equation $(ii)$ are identical for any value of $\lambda$,the bisectors are coincident for any real number $\lambda$.

If the bisectors of the angles between the pairs of lines given by the equations $ax^2 + 2hxy + by^2 = 0$ and $ax^2 + 2hxy + by^2 + \lambda(x^2 + y^2) = 0$ are coincident,then $\lambda = $

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