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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

Paragraph: Through point O a straight line L₁ is drawn to cut two given straight lines 3 x+4 y-5=0 and x+2 y-3=0 at the points L & M , where O is origin. On the basis of above information answer the following : Question: The equation of the angle bisector between two given lines which will contain the point (2,3) is -

Options

  1. A(3+ 5 ) x+2(2- 5 ) y+ 5 (3+ 5 )=0
  2. B(3- 5 ) x+2(2- 5 ) y+ 5 (3- 5 )=0
  3. C(3+ 5 ) x+2(2+ 5 ) y+ 5 (3+ 5 )=0
  4. D(3- 5 ) x-2(2+ 5 ) y- 5 (3- 5 )=0

Correct answer

B. (3- 5 ) x+2(2- 5 ) y+ 5 (3- 5 )=0

Step-by-step solution

Let equation of straight line through O is x = y =r Let OL = r ₁ and OM = r ₂ , then the coordinates of L and M are given by L ( r ₁ , r ₁ ) and m ( r ₂ , r ₂ ) . Let N(h, k) be the variable point such that O N=r₃ , then h=r₃ , k=r₃ , since L and M lie on 3 x+4 y-5=0 and x+2 y-3=0 so r₁(3 +4 )=5 and r₂( +2 )=3 r ₁ r ₃ = 5 3 ~h +4 k and r ₂ r ₃ = 3 ~h +2 k 3 x+4 y-5 5 = x+2 y-3 5 Now 3(2)+4(3)-5 0 and 2+2(3)-3 0 so ' + ' sign bisector will contain the point (2,3) aligned & 3 x+4 y-5= 5 x+2 5 y-3 5 & (3- 5 ) x+2(2- 5

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