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COMEDK2019MathematicsStraight 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

We have, equation of line x a + y b =1 . Let P(h, k) be the required point. Now, coordinates A and B are (a, 0) and (0, b) respectively. Since, P is mid-point of A B . Therefore, (h, k)= ( a+0 2 , 0+b 2 ) h= a 2 and k= b 2 a=2 h and b=2 k Now, it is given that aligned & a+b=4 & 2 h+2 k=4 & h+k=2 aligned So, locus of P is x+y=2

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