Q209 / 270 · NDA 2021 (Phase 1) · Mathematics

If $A, B$ and $C$ are in AP , then the straight line $A x+2 B y+C=0$ will always pass through a fixed point. The fixed point is

  • A
    $(0,0)$
  • B
    $(-1,1)$
  • C
    $(1,-2)$
  • Correct answer
    D
    $(1,-1)$

Solution

As $A, B$ and $C$ are in A.P. $\therefore 2 B=A+C \Rightarrow A-2 B+C=0$ From given equation $A x+2 B y+C=0$. For $(x, y)=(1,-1), A-2 B+C=0$ Hence, line always passes through $(1,-1)$.

Hence, the correct answer is option: 'D'.

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