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KCET2008MathematicsStraight Lines

A variable line x a + y b =1 is such that a+b=4 . The locus of the mid point of the portion of the line intercepted between the axes is

Options

  1. Ax+y=4
  2. Bx+y=8
  3. Cx+y=1
  4. Dx+y=2

Correct answer

D. x+y=2

Step-by-step solution

Let the coordinate of mid point of A B is (x₁, y₁ ) . aligned & x ₁= a +0 2 , y ₁= 0+ b 2 & a =2 x ₁, ~b =2 y ₁ & Given, a ₁+2 ~b ₁=4 & x ₁+ y ₁=2 aligned Hence, the locus of the mid point is x+y=2

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