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JEE 2024 Mathematics PYQ — The portion of the line 4x + 5y = 20 in the first quadrant is tri… | Mathem Solvex | Mathem Solvex

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JEE 2024 — Mathematics PYQ

JEE | Mathematics | 2024

The portion of the line 4x + 5y = 20 in the first quadrant is trisected by the lines L₁ and
L₂ passing through the origin. The tangent of an angle between the lines L₁ and L₂ is :

Choose the correct answer:

A.
8/5
B.
25/41
C.
2/5
D.
30/41
(Correct Answer)

Correct Answer:

30/41

Explanation

The given line is 4x + 5y = 20

and $m_{2} (QO) = \frac{\frac{4}{3}}{\frac{10}{3}} = \frac{4}{10} = \frac{2}{5}$

$∴ tan θ = \frac{\frac{8}{5} - \frac{2}{5}}{1 + \frac{16}{25}} = \frac{\frac{6}{5}}{\frac{41}{25}} = \frac{30}{41}$

Explanation

The given line is 4x + 5y = 20

and $m_{2} (QO) = \frac{\frac{4}{3}}{\frac{10}{3}} = \frac{4}{10} = \frac{2}{5}$

$∴ tan θ = \frac{\frac{8}{5} - \frac{2}{5}}{1 + \frac{16}{25}} = \frac{\frac{6}{5}}{\frac{41}{25}} = \frac{30}{41}$

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