Let the angles made with the positive x -axis by two straight lines drawn from the point P (2,3) and meeting the line x + y =6 at a distance √(2/3) from the point P be θ 1 and θ 2 . Then the value of (θ 1 +θ 2 ) is :

Mathematics · Straight lines

JEE Main 2026 — 24 January, Evening Shift — Question 3

Let the angles made with the positive $x$ -axis by two straight lines drawn from the point $\mathrm{P}(2,3)$ and meeting the line $\mathrm{x}+\mathrm{y}=6$ at a distance $\sqrt{\frac{2}{3}}$ from the point P be $\theta_{1}$ and $\theta_{2}$ . Then the value of $\left(\theta_{1}+\theta_{2}\right)$ is :

Option A:
$\frac{\pi}{12}$
Option B:
$\frac{\pi}{6}$
Option C:
$\frac{\pi}{2}$
Correct
Option D:
$\frac{\pi}{3}$

Answer: C

Step-by-step solution

Let Q is $\left(\sqrt{\frac{2}{3}} \cos \theta+2, \sqrt{\frac{2}{3}} \sin \theta+3\right)$

So, $x+y=6$

$\sqrt{\frac{2}{3}}(\cos \theta+\sin \theta)+5=6$

$\sin \theta+\cos \theta=\sqrt{\frac{3}{2}}$

$1+\sin 2 \theta=\frac{3}{2}$

$\sin 2 \theta=\frac{1}{2}$

$2 \theta=\frac{\pi}{6}, \frac{5 \pi}{6}$

$2\theta=\frac{\pi}{6}$ and $\frac{5 \pi}{6}$

So $\theta_{1}+\theta_{2}=\frac{\pi}{2}$

Answer key and solution verified before publishing.

Practise Straight lines

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 24 January, Evening Shift
Subject: Mathematics
Chapter: Straight lines
Topic: Angle bisectors, concurrent lines.

The sum of all values of alpha , for which the shortest distance between the lines frac x+1alpha=frac y-2-1=frac z-4-alpha and frac…

Answer: C

Step-by-step solution

Practise Straight lines

More Straight lines questions from this paper