A) \[\frac{35}{\sqrt{34}}\]
B) \[\frac{1}{3\sqrt{34}}\]
C) \[\frac{35}{3\sqrt{34}}\]
D) \[\frac{35}{2\sqrt{34}}\]
Correct Answer: C
Solution :
Given lines are \[5x+3y-7=0\] .....(i) and \[15x+9y+14=0\] or \[5x+3y+\frac{14}{3}=0\] .....(ii) lines (i) and (ii) are parallel. Since \[{{c}_{1}}\] and \[{{c}_{2}}\] are of opposite signs, therefore the lines are on opposite sides of the origin. So the distance between them is \[=\left| \frac{{{c}_{1}}}{\sqrt{a_{1}^{2}+b_{1}^{2}}} \right|+\left| \frac{{{c}_{2}}}{\sqrt{a_{2}^{2}+{{b}_{2}}}} \right|\]\[=\left| \frac{-7}{\sqrt{34}} \right|+\left| \frac{14}{3\sqrt{34}} \right|\]\[=\frac{35}{3\sqrt{34}}.\]
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