Straight Line and Pair of Straight Lines 1 Question 3

3. Lines are drawn parallel to the line 4x3y+2=0, at a distance 35 from the origin. Then which one of the following points lies on any of these lines?

(2019 Main, 10 April I)

(a) 14,23

(b) 14,23

(c) 14,13

(d) 14,13

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Solution:

  1. Since, equation of a line parallel to line ax+by+c=0 is ax+by+k=0

Equation of line parallel to line

4x3y+2=0 is 4x3y+k=0

Now, distance of line (i) from the origin is

|k|42+32=35

|k|=3k=±3

So, possible lines having equation, either 4x3y+3=0 or 4x3y3=0

Now, from the given options the point 14,23 lies on the line 4x3y+3=0.



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