AP EAMCET · Maths · Straight Lines
\(2 x^2-3 x y-2 y^2=0\) represents two lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\). \(2 x^2-3 x y-2 y^2-x+7 y-3=0\) represents another two lines \(\mathrm{L}_3\) and \(\mathrm{L}_4\). Let A be the point of intersection of lines \(\mathrm{L}_1\), \(L_3\) and \(B\) be the point of intersection of lines \(L_2\) and \(L_4\). The area of the triangle formed by lines \(A B\) and \(L_3, L_4\) is
- A \(\frac{3}{10}\)
- B \(\frac{3}{5}\)
- C \(\frac{15}{2}\)
- D \(\frac{5}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{10}\)
Step-by-step Solution
Detailed explanation
Given the equation \(2 x^2-3 x y-2 y^2=0 \Rightarrow(2 x+y)(x-2 y)=0\) Let \(\mathrm{L}_1: 2 x+y=0, \mathrm{~L}_2: x-2 y=0\) \(\begin{aligned} & \text { and } 2 x^2-3 x y-2 y^2-x+7 y-3=0 \\ & \Rightarrow(2 x+y-1)(x-2 y+3)=0\end{aligned}\) Let…
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