A) \[2x-y-7=0,\,2x+y-9=0\]
B) \[2x+y+7=0,\,2x+y+9=0\]
C) \[2x+y-7=0,\,\,2x+y+9=0\]
D) \[2x-y+7=0,\,2x-y+9=0\]
Correct Answer: A
Solution :
The abscissa of point is found by substituting the ordinates and solving for abscissa. \[\Rightarrow {{x}^{2}}-8x+15=0\] \[\Rightarrow x=\frac{8\pm \sqrt{64-60}}{2}=\frac{8\pm 2}{2}=5\] or 3 i.e., points are \[(5,\ -1)\]and (3,?1). Normal is given by, \[\frac{x-5}{5-4}=\frac{y+1}{-1-1}\Rightarrow 2x+y-9=0\] and \[\frac{x-3}{3-4}=\frac{y+1}{-1-1}\Rightarrow 2x-y-7=0\].
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