TS EAMCET · Maths · Pair of Lines
For integer \(k\), if the area of the triangle formed by the pair of lines \(S=3 x^2-2 k x y+y^2=0\) with the line \(L=2 x-y-6=0\) is 36 sq. units, then for the angle \(\theta\) between the lines \(S=0, \sin \theta=\)
- A \(\frac{1}{2}\)
- B \(\frac{\sqrt{3}}{2}\)
- C \(\frac{1}{\sqrt{3}}\)
- D \(\frac{1}{\sqrt{5}}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\sqrt{5}}\)
Step-by-step Solution
Detailed explanation
Equation of given pair of straight lines \(S=3 x^2-2 k x y+y^2=0\) and the line \(L=2 x-y-6=0\) On solving, we get \(3 x^2-2 k x(2 x-6)+(2 x-6)^2=0\) \(\Rightarrow \quad(7-4 k) x^2+12(k-2) x+36=0\) Let the intersection points are \(A\left(x_1, y_1\right)\) and…
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