Mathematics · Straight lines

JEE Main 2025 — 28 January, Evening Shift — Question 17

Two equal sides of an isosceles triangle are along $-x+2 y=4$ and $x+y=4$ . If $m$ is the slope of its third side, then the sum of all possible distinct values of m , is :

Option A:
$-6$
Option B:
12
Option C:
6
Correct
Option D:
$-2 \sqrt{10}$

Answer: C

Step-by-step solution

$\tan \theta=\frac{m-\frac{1}{2}}{1+\frac{1}{2} \cdot m}=\frac{-1-m}{1-m}$

$\frac{2 \mathrm{~m}-1}{2+\mathrm{m}}=\frac{\mathrm{m}+1}{\mathrm{~m}-1}$

$2 \mathrm{~m}^{2}-3 \mathrm{~m}+1=\mathrm{m}^{2}+3 \mathrm{~m}+2$

$\mathrm{m}^{2}-6 \mathrm{~m}-1=0$

sum of root $=6$

sum is 6

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 28 January, Evening Shift
Subject: Mathematics
Chapter: Straight lines
Topic: Angle between lines, perpendicular distance & distance between parallel lines, foot, image

Let A, B, C be three points in xy-plane, whose position vector are given by √(3) hati+hatj, hati+√(3) hatj and a hati+(1-a) hatj…

Answer: C

Step-by-step solution

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