A) \[4\sqrt{2}\]
B) \[2\sqrt{2}\]
C) \[8\]
D) \[8\sqrt{2}\]
Correct Answer: D
Solution :
Equations of given lines \[x+y=8\] ...(i) and \[x+y=12\] ...(ii) Both of these lines are mutually perpendicular \[\therefore \]Distance between the parallel lines \[\left| \frac{{{c}_{1}}-{{c}_{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|=\left| \frac{12-8}{\sqrt{1+1}} \right|\] \[=\frac{4}{\sqrt{2}}=2\sqrt{2}\] \[\therefore \] \[a=2\sqrt{2}\] Hence, length of latusrectum\[=4a\] \[=4\times 2\sqrt{2}=8\sqrt{2}\]
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