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AP EAMCET2010MathematicsStraight Lines

A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the straight line y=2 x+3+ 2 at (x₀, y₀ ) . Then 2 x₀+y₀ is equal to

Options

  1. A3+ 2
  2. B2 -1
  3. C1
  4. D0

Correct answer

B. 2 -1

Step-by-step solution

The equation of line A B which makes an equal intercepts on positive x and y axes are x a + y a =1 ie, x+y=a ...(i) Distance of Eq. (i) from origin =1 | 0+0-a 1+1 |=1, -a 2 =1 a= 2 From Eq. (i), x+y= 2 ...(ii) Also given line, 2 x-y=-3- 2 ...(iii) The intersection point of line (ii) and line (iii) is (x₀, y₀ )=(-1, 2 +1) So, 2 x₀+y₀=2(-1)+ 2 +1=-2+ 2 +1=( 2 -1) Hence, 2 x₀+y₀= 2 -1

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