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9.Straight Line
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Three lines $x + 2y + 3 = 0 ; x + 2y - 7 = 0$ and $2x - y - 4 = 0$ form the three sides of two squares. The equation to the fourth side of each square is
A
$2x - y + 14 = 0\,\,\, ane\,\, \,2x - y + 6 = 0$
B
$2x - y + 14 = 0\,\,\, ane\,\, \,2x - y - 6 = 0$
C
$2x - y - 14 = 0\,\,\, ane\,\, \,2x - y - 6 = 0$
D
$2x - y - 14 = 0\, ane \,2x - y + 6 = 0$
Solution
$d = \left| {\,\frac{{10}}{{\sqrt 5 }}\,} \right|$
$3^{rd}$ side is parallel to the line $2x – y – 4 = 0$
Hence line is $2x – y + \lambda = 0$
now $\left| {\frac{{\lambda + 4}}{{\sqrt 5 }}} \right|$$= \frac{{10}}{{\sqrt 5 }}$
$\lambda + 4 = \pm 10$
$\lambda = 6$ or $\lambda = – 14 \Rightarrow (B)$
Standard 11
Mathematics
