AP EAMCET · Maths · Pair of Lines
Which among the following represents the combined equation of a pair of lines through point \((1,0)\) and parallel to the lines represented by \(2 x^2-x y-y^2=0\).
- A \(2 x^2-x y-2 y^2+4 x-y=6\)
- B \(2 x^2-x y-y^2-4 x+y+2=0\)
- C \(2 x^2-x y-2 y^2-4 x+y+2=0\)
- D \(2 x^2-x y-y^2-4 x-y=2\)
Answer & Solution
Correct Answer
(B) \(2 x^2-x y-y^2-4 x+y+2=0\)
Step-by-step Solution
Detailed explanation
Given line, \(2 x^2-x y-y^2=0...(i)\) \(\begin{aligned} \Rightarrow \quad 2 x^2-2 x y+x y-y^2 & =0 \\ 2 x(x-y)+y(x-y) & =0 \\ (2 x+y)(x-y) & =0\end{aligned}\) Since, we have given that combined equation of the pair is parallel to \(2 x^2-x y-y^2=0\) So, combined equation will be…
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