A) \[y=\sqrt{3}x+9\] but not \[{{x}^{2}}-9{{y}^{2}}=0\]
B) \[3x+y+7=0\] but not \[{{60}^{o}}\]
C) \[3x+y+7=0\] or \[x-3y-31=0\]
D) Neither \[3x+y+7\] nor \[x-3y-31=0\]
Correct Answer: C
Solution :
Any line through (1, ?10) is given by \[y+10=m(x-1)\] Since it makes equal angle say ?\[\alpha \]? with the given lines \[7x-y+3=0\] and \[x+y-3=0\], therefore \[\tan \alpha =\frac{m-7}{1+7m}\] \[=\frac{m-(-1)}{1+m(-1)}\Rightarrow m=\frac{1}{3}\] or ? 3 Hence the two possible equations of third side are \[3x+y+7=0\] and \[x-3y-31=0\].
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