TS EAMCET · Maths · Pair of Lines
The acute angle between the pair of straight lines joining the origin to the points of intersection of the line \(x+y-1=0\) with the pair of straight lines \(k x^2+8 x y-3 y^2+2 x-4 y-1=0\) is
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{4}\)
- C \(\cos ^{-1}\left(\frac{1}{\sqrt{10}}\right)\)
- D \(\cos ^{-1}\left(\frac{3}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(C) \(\cos ^{-1}\left(\frac{1}{\sqrt{10}}\right)\)
Step-by-step Solution
Detailed explanation
We have, \(k x^2+8 x y-3 y^2+2 x-4 y-1=0\) is form of a straight line \(\begin{array}{r} \therefore \quad\left|\begin{array}{ccc} k & 4 & 1 \\ 4 & -3 & -2 \\ 1 & -2 & -1 \end{array}\right|=0 \\ k(3-4)-4(-4+2)+1(-8+3)=0 \\ -k+8-5=0 \Rightarrow k=3 \end{array}\) \(\therefore\)…
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