The equation of lines passing through \((5,3)\) and perpendicular to \(2 x+y-7=0\) is

The equation of lines passing through \((5,3)\) and perpendicular to \(2 x+y-7=0\) is
  1. \(2 y-x-2=0\)
  2. \(2 y-x+2=0\)
  3. \(x+y-8=0\)
  4. \(2 y-x-1=0\)

Solution

\(2 x+y+7=0 \Rightarrow P=(5,3)\) Required line is \(b\left(x-x_1\right)-a\left(y-y_1\right)=0\) \(\begin{aligned} 1(x-5)-2(y-3) & =0 \\ x-5-2 y+6 & =0 \\ x-2 y+1 & =0 \\ \Rightarrow 2 y-x-1 & =0 \end{aligned}\) Hence, option (d) is correct.

Asked in: AP EAMCET 2020 (18 Sep Shift 2)

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