Q63 / 200 · AP EAMCET 2001 · Mathematics

For all values of $a$ and $b$ the line $(a+2 b) x+(a-b) y+(a+5 b)=0$ passes through the point.

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

Solution

Let the line passes through a point whose coordinates are $(-2,1)$, then $\begin{aligned}(a & +2 b)(-2)+(a-b)(1)+a+5 b \\ & =-2 a-4 b+a-b+a+5 b \\ & =-2 a-5 b+2 a+5 b \\ & =0\end{aligned}$ $\therefore$ Our assumption is true. The required point is $(-2,1)$

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

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