AP EAMCET · Maths · Straight Lines
If the lines \(x+y-2=0,3 x-4 y+1=0\) and \(5 x+k y-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(\mathrm{kx}+\mathrm{y}-\mathrm{k}=0\) is
- A \(x-3 y=-2\)
- B \(x+4 y=5\)
- C \(x+6 y=7\)
- D \(x-2 y=-1\)
Answer & Solution
Correct Answer
(D) \(x-2 y=-1\)
Step-by-step Solution
Detailed explanation
\(x+y=2 \quad (1)\) \(3x-4y=-1 \quad (2)\) \(4 \times (1) + (2) \Rightarrow 7x=7 \Rightarrow x=1\) \(y=2-x = 2-1 = 1\) \((\alpha, \beta) = (1, 1)\) \(5x+ky-7=0 \Rightarrow 5(1)+k(1)-7=0 \Rightarrow k-2=0 \Rightarrow k=2\) Line perpendicular to \(kx+y-k=0 \equiv 2x+y-2=0\) has…
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