TS EAMCET · Maths · Pair of Lines
If the pair of straight lines \(x y-x-y+1=0\) and the line \(x+a y-3=0\) are concurrent, then the acute angle between the pair of lines \(a x^2-13 x y-7 y^2+x+23 y-6=0\) is
- A \(\cos ^{-1}\left(\frac{5}{\sqrt{218}}\right)\)
- B \(\cos ^{-1}\left(\frac{1}{\sqrt{10}}\right)\)
- C \(\cos ^{-1}\left(\frac{5}{\sqrt{173}}\right)\)
- D \(\cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)\)
Answer & Solution
Correct Answer
(B) \(\cos ^{-1}\left(\frac{1}{\sqrt{10}}\right)\)
Step-by-step Solution
Detailed explanation
Given equations of pair of straight lines, \(x y-x-y+1=0\) can be rewritten as \(\begin{aligned} & x(y-1)-1(y-1)=0 \\ & \Rightarrow \quad(x-1)(y-1)=0 \\ & \Rightarrow \quad x=1 \text { and } y=1 \\ & \end{aligned}\) Thus, the three concurrent lines are…
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