Q51 / 160 · WBJEE 2011 · Mathematics

If the three points \(A(1,6), B(3,-4)\) and \(C(x, y)\) are collinear then the equation satisfying by \(x\) and \(y\) is

  • Correct answer
    A
    \(5 x+y-11=0\)
  • B
    \(5 x+13 y+5=0\)
  • C
    \(5 x-13 y+5=0\)
  • D
    \(13 x-5 y+5=0\)

Solution

\(\begin{aligned} & \text {Hints: }\left|\begin{array}{ccc} 1 & 1 & 6 \\ 1 & 3 & -4 \\ 1 & x & y \end{array}\right|=0 \\ & \Rightarrow 1(3 y+4 x)-(y-6 x)+1(-4-18)=0 \Rightarrow 3 y+4 x-y+6 x-12=0 \\ & \Rightarrow 2 y+10 x-22=0 \\ & y+5 x=11 \end{aligned}\)

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

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