Mathematics · Straight lines

JEE Main 2026 — 8 April, Evening Shift — Question 28

If a straight line drawn through the point of intersection of the lines $4x+3y-1=0$ and $3x+4y-1=0,$ meet the coordinate axes at points P and Q, then the locus of the mid point of PQ is :

Option A:
$x+y-7=0$
Option B:
$x+y-14xy=0$
Correct
Option C:
$2x+y+14xy=0$
Option D:
$x+2y-14xy=0$

Answer: B

Step-by-step solution

Point of intersection of the lines $3 x+4 y=1$ and $4 x+3 y=1$ is $\left(\frac{1}{7}, \frac{1}{7}\right)$ Let the line be $\frac{x}{2 h}+\frac{y}{2 k}=1$ Satisfy $\left(\frac{1}{7}, \frac{1}{7}\right)$ $\frac{1}{14 h}+\frac{1}{14 k}=1$ $\frac{1}{x}+\frac{1}{y}=14$

$x+y-14xy=0$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 8 April, Evening Shift
Subject: Mathematics
Chapter: Straight lines
Topic: Various forms of lines