A) equally inclined
B) perpendicular
C) bisector of the angle
D) None of the above
Correct Answer: A
Solution :
If the two pairs of straight lines have the same bisectors, then the two pairs are equally inclined. The equation of the bisectors of the angle between the lines given by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{xy}{h}\] ? (i) The equation of the bisectors of the angle between the lines given by \[{{a}^{2}}{{x}^{2}}+2h(a+b)xy+{{b}^{2}}{{y}^{2}}=0\]is \[\Rightarrow \] \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{xy}{h}\] ? (ii) Clearly Eqs. (i) and (ii) are the same. The two pairs of straight lines are equally inclined.
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