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