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JEE Main 20248 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2024 · 8 April · Evening Shift · Mathematics · Straight Lines

If the line segment joining the points (5,2) and (2, a) subtends an...

If the line segment joining the points (5,2)(5,2) and (2,a)(2, a) subtends an angle π4\frac{\pi}{4} at the origin, then the absolute value of the product of all possible values of aa is :If the line segment joining the points (5,2) and (2, a) subtends an angle (π)/(4) at the origin, then the absoluteIf the line segment joining the points (5,2) and (2, a) subtends an angle (π)/(4) at the origin, then the absolute

Options

  1. A6
  2. B8
  3. C2
  4. D-4

Correct answer

D. -4

Step-by-step solution

If the line segment joining the points (5,2) and (2, a) subtends an angle (π)/(4) at the origin, then the absolute
mOA=25 mOB=a2\begin{aligned} & \mathrm{m}_{\mathrm{OA}}=\frac{2}{5} \\ & \mathrm{~m}_{\mathrm{OB}}=\frac{\mathrm{a}}{2}\end{aligned}tan⁡π4=∣25−a2∣1=∣4−5a10+2a∣\begin{aligned} & \tan \frac{\pi}{4}=\left|\frac{2}{5}-\frac{a}{2}\right| \\ & 1=\left|\frac{4-5 a}{10+2 a}\right|\end{aligned}$If the line segment joining the points (5,2) and (2, a) subtends an angle (π)/(4) at the origin, then the absolute
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