SATHEE: Straight Line Question 108

Straight Line Question 108

Question: Distance between the lines $ 5x+3y-7=0 $ and $ 15x+9y+14=0 $ is [Kerala (Engg.) 2002]

Options:

A) $ \frac{35}{\sqrt{34}} $

B) $ \frac{1}{3\sqrt{34}} $

C) $ \frac{35}{3\sqrt{34}} $

D) $ \frac{35}{2\sqrt{34}} $

Show Answer

Answer:

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 $ =| \frac{c_1}{\sqrt{a_1^{2}+b_1^{2}}} |+| \frac{c_2}{\sqrt{a_2^{2}+b_2}} | $ $ =| \frac{-7}{\sqrt{34}} |+| \frac{14}{3\sqrt{34}} | $ $ =\frac{35}{3\sqrt{34}}. $

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Straight Line Question 108

Question: Distance between the lines $ 5x+3y-7=0 $ and $ 15x+9y+14=0 $ is [Kerala (Engg.) 2002]

Options:

Answer:

Solution:

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