QJEEM21Maba69: JEE Main 2021 Mathematics - Class 11 JEEM21Maba69 Solution: The equation of one of the straight lines which passes through…

Question

Verified Solution • 2025–26 Session moderate

The equation of one of the straight lines which passes through the point (1, 3) and makes an angles

\tan^{- 1} (\sqrt{2})

with the straight line, y + 1 = 3

\sqrt{2}

x is :

Accepted Answer

Let slope of line be m

∴

| \frac{m - 3 \sqrt{2}}{1 + 3 \sqrt{2} m} | = \sqrt{2}

\Rightarrow m - 3 \sqrt{2} = \pm \sqrt{2} \pm 6 m

\Rightarrow m \mp 6 m = \pm \sqrt{2} + 3 \sqrt{2}

\Rightarrow m = - \frac{4 \sqrt{2}}{5}

or

\frac{2 \sqrt{2}}{7}

Hence line can be

y - 3 = \frac{- 4 \sqrt{2}}{5} (x - 1)

\Rightarrow 5 y - 15 = - 4 \sqrt{2} x + 4 \sqrt{2}

\Rightarrow 4 \sqrt{2} x + 5 y - (15 + 4 \sqrt{2}) = 0

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