TS EAMCET · Maths · Straight Lines
Let the line \(2 x-3 y-1=0\) intersect the curve \(x^2+2 x y+\) \(5 y^2+2 x+3 y-1=0\) in distinct points A and B. If 'O' is the origin, then \(\cos \angle \mathrm{AOB}=\)
- A \(\frac{1}{2}\)
- B \(\frac{3 \sqrt{2}}{5}\)
- C 0
- D \(\frac{3 \sqrt{2}}{7}\)
Answer & Solution
Correct Answer
(D) \(\frac{3 \sqrt{2}}{7}\)
Step-by-step Solution
Detailed explanation
\text { } \begin{aligned} & 2 x-3 y-1=0 \Rightarrow 2 x-3 y=1 \\ \Rightarrow & x^2+2 x y+5 y^2+2 x-1+3 y \cdot 1-(1)^2=0 \\ \Rightarrow & x^2+2 x y+5 y^2+2 x(2 x-3 y) \\ & +3 y(2 x-3 y)-(2 x-3 y)^2=0 \\ \Rightarrow & x^2+2 x y+5 y^2+4 x^2-6 x y+6 x y \\ & -9 y^2-4 x^2-9 y^2+12 x…
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