Straight Line and Pair of Straight Lines 1 Question 23

23. A straight line L through the point (3,2) is inclined at an angle 60 to the line 3x+y=1. If L also intersects the X-axis, then the equation of L is

(2011)

(a) y+3x+233=0

(b) y3x+2+33=0

(c) 3yx+3+23=0

(d) 3y+x3+23=0

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Solution:

  1. A straight line passing through P and making an angle of α=60, is given by

yy1xx1=tan(θ±α)

3x+y=1

y=3x+1, then tanθ=3

y+2x3=tanθ±tanα1tanθtanαy+2x3=3+31(3)(3)

 and y+2x3=331+(3)(3)y+2x3=0 and =2313=3y+2=3x33

Neglecting, y+2=0, as it does not intersect Y-axis.



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