A) 1
B) \[-1\]
C) 2
D) \[-2\]
Correct Answer: C
Solution :
Let\[{{m}_{1}}\]and\[{{m}_{2}}\]be the slopes of lines represented by\[a{{x}^{2}}+2hxy+b{{y}^{2}}=0,\]then \[{{m}_{1}}+{{m}_{2}}=-\frac{2h}{b}\]and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] The given pair of lines is \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] On comparing with\[a{{x}^{2}}+2\text{ }hxy+b{{y}^{2}}=0,\]we get \[a=1,2h=-2c,b=-7\] \[{{m}_{1}}+{{m}_{2}}=-\frac{2h}{b}=-\frac{2c}{7}\] and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}=-\frac{1}{7}\] Given that, \[{{m}_{1}}{{m}_{2}}=4{{m}_{1}}{{m}_{2}}\] \[\Rightarrow \] \[-\frac{2c}{7}=-\frac{4}{7}\] \[\Rightarrow \] \[c=\frac{4}{2}=2\]
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