Straight Line and Pair of Straight Lines 1 Question 51

51. A straight line L through the origin meets the line x+y=1 and x+y=3 at P and Q respectively. Through P and Q two straight lines L1 and L2 are drawn, parallel to 2x−y=5 and 3x+y=5, respectively. Lines L1 and L2 intersect at R, show that the locus of R as L varies, is a straight line.

(2002,5 M)

Show Answer

Solution:

  1. Let the equation of straight line L be

Q≡3m+1,3mm+1

Now, equation of

L1:y−2x=m−2m+1

and equation of

L2:y+3x=3m+9m+1

By eliminating m from Eqs. (i) and (ii), we get locus of R as x−3y+5=0, which represents a straight line.

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