A) \[a+b=-\frac{2}{7}\]
B) Area of the triangle formed by the line \[ax+by+2=0\]with coordinate axes is\[\frac{14}{5}\].
C) Line \[ax+by+3=0\]always passes through the point\[(-1,1)\].
D) Max \[\{a,b\}=\frac{5}{7}\]
Correct Answer: C
Solution :
[c] Line \[ax+by+2=0\] passes through the point \[\left( 2,\frac{8}{3} \right)\]. \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,6a+8b+6=0\] or \[3a+4b+3=0\] ?...(1) Now, \[bx-ay+4=0\]and \[3x+4y+5=0\] meet axes in concyclic points. So, \[{{m}_{1}}{{m}_{2}}=1\] \[\left( \frac{b}{a} \right).\left( -\frac{3}{4} \right)=1\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,4a+3b=0\] ?...(2) Solving (1) and (2), we get a\[~a=9/7,\text{ }b=-12/7\] Therefore, line \[ax+by+3=0\]always passes through the point \[(-1,1)\].
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