JEE Mains · Maths · STD 11 - 9. straight line
The distance between the two points \(A\) and \(A ^{\prime}\) which lie on \(y =2\) such that both the line segments \(AB\) and \(A ^{\prime} B\) (where \(B\) is the point \((2,3)\) ) subtend angle \(\frac{\pi}{4}\) at the origin, is equal to
- A \(10\)
- B \(\frac{48}{5}\)
- C \(\frac{52}{5}\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(\frac{52}{5}\)
Step-by-step Solution
Detailed explanation
\(M_{1}=3 / 2 \quad M_{2}=2 / x\) \(\tan \pi / 4=\left|\frac{3 / 2-2 / x}{1+6 / 2 x}\right|=1\) \(\Rightarrow x_{1}=10, \quad x_{2}=-2 / 5\) \(\Rightarrow AA ^{1}=52 / 5\)
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