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AP EAMCET2001MathematicsStraight Lines

The lines 2 x+3 y=6,2 x+3 y=8 cut the X -axis at A and B , respectively. A line L drawn through the point (2,2) meets the X -axis as C in such a way that abscissae of A, B and C are in arithmetic progression. Then, the equation of the line L is

Options

  1. A2 x+3 y=10
  2. B8 x+2 y=10
  3. C2 x-3 y=10
  4. D8 x-2 y=10

Correct answer

A. 2 x+3 y=10

Step-by-step solution

Given lines are 2 x+3 y=6 and 2 x+3 y=8 These lines meet the X -axis at A(3,0) and B(4,0) . The line L passes through (2,2) cuts X -axis at C , such that x -coordinate of A, B, C are in ap i.e. 3,4, x₁ array ll & 2.4=3+x₁ & x₁=8-3=5 array To coordinates of C are (5,0) . A line L passing through the points (2,2) and (5,0) , is aligned & y-0 & = 0-2 5-2 (x-5) & y & = -2 3 (x-5) & 3 y & =-2 x+10 & 2 x+3 y & =10 aligned

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