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Question

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

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$(a - b)h' = (a' - b')h$

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(A) The equation of the pair of angle bisectors for the pair of lines $ax^2 + 2hxy + by^2 = 0$ is given by $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$.For the first pair,the equation of bisectors is $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$.For the second pair,the equation of bisectors is $\frac{x^2 - y^2}{a' - b'} = \frac{xy}{h'}$.Since the bisectors are the same,the ratios of the coefficients must be equal:$\frac{a - b}{h} = \frac{a' - b'}{h'}$.Cross-multiplying gives: $(a - b)h' = (a' - b')h$.

If the bisectors of the angles represented by $ax^2 + 2hxy + by^2 = 0$ and $a'x^2 + 2h'xy + b'y^2 = 0$ are the same,then:

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