JEE Mains · Maths · STD 11 - 9. straight line
If the line segment joining the points \((5,2)\) and \((2, a)\) subtends an angle \(\frac{\pi}{4}\) at the origin, then the absolute value of the product of all possible values of \(a\) is:
- A \(6\)
- B \(8\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\( \mathrm{m}_{\mathrm{OA}}=\frac{2}{5} \) \( \mathrm{~m}_{\mathrm{OB}}=\frac{\mathrm{a}}{2}\) \(\tan \frac{\pi}{4}=\left|\frac{2}{5}-\frac{a}{2}\right|\) \(1=\left|\frac{4-5 a}{10+2 a}\right|\) \(4-5 \mathrm{a}= \pm(10+2 \mathrm{a}) \) \(4-5 \mathrm{a}=10+2 \mathrm{a} \)…
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