(B) Let the line intersect the $x$-axis at $Q(a, 0)$ and the $y$-axis at $P(0, b)$.Since the point $A(3, 4)$ bisects the intercept $PQ$,it is the midp

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Let the line intersect the $x$-axis at $Q(a, 0)$ and the $y$-axis at $P(0, b)$.Since the point $A(3, 4)$ bisects the intercept $PQ$,it is the midpoint of $PQ$.Using the midpoint formula:$\frac{a + 0}{2} = 3 \implies a = 6$$\frac{0 + b}{2} = 4 \implies b = 8$The intercept form of the equation of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values of $a$ and $b$:$\frac{x}{6} + \frac{y}{8} = 1$Multiplying by $24$ to clear the denominators:$4x + 3y = 24$

Class 11 Mathematics Straight Lines Slope of line, Equation of line in different forms

Medium

$A$ straight line passes through the point $A(3, 4)$ such that its intercept between the axes is bisected at $A$. Find its equation.

AIEEE 2006 All AIEEE

A
$3x - 4y + 7 = 0$
B
$4x + 3y = 24$
C
$3x + 4y = 25$
D
$x + y = 7$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Lines

Subtopic

Slope of line, Equation of line in different forms

Previous Year

AIEEE 2006 Paper All AIEEE years →

$A$ graph is drawn between the $y-x$ axes. Which of the following equations is correct for the graph?

Medium

View Solution

If the point $(3, -4)$ divides the segment of the line between the $X$-axis and $Y$-axis in the ratio $2 : 3$,then the equation of the line is:

Medium

View Solution

If a straight line passing through the point $P(-3, 4)$ is such that its intercepted portion between the coordinate axes is bisected at $P,$ then its equation is

DifficultJEE MAIN 2019

View Solution

If a straight line passes through the point $(-5, 4)$ and makes an intercept of length $\frac{2}{\sqrt{5}}$ between the lines $x+2y+1=0$ and $x+2y-1=0$,then the equation of that line is

EasyTS EAMCET 2019

View Solution

The equation of the line,passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \cos \theta - y \sin \theta = a$,is

EasyAP EAMCET 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ straight line passes through the point $A(3, 4)$ such that its intercept between the axes is bisected at $A$. Find its equation.

Similar Questions

$A$ graph is drawn between the $y-x$ axes. Which of the following equations is correct for the graph?

If the point $(3, -4)$ divides the segment of the line between the $X$-axis and $Y$-axis in the ratio $2 : 3$,then the equation of the line is:

If a straight line passing through the point $P(-3, 4)$ is such that its intercepted portion between the coordinate axes is bisected at $P,$ then its equation is

If a straight line passes through the point $(-5, 4)$ and makes an intercept of length $\frac{2}{\sqrt{5}}$ between the lines $x+2y+1=0$ and $x+2y-1=0$,then the equation of that line is

The equation of the line,passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \cos \theta - y \sin \theta = a$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module