(B) Let the line be $L(x, y) = 3x - 5y + a = 0$. For two points $(x_1, y_1)$ and $(x_2, y_2)$ to lie on the same side of the line $Ax + By + C = 0$,th

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

(B) Let the line be $L(x, y) = 3x - 5y + a = 0$. For two points $(x_1, y_1)$ and $(x_2, y_2)$ to lie on the same side of the line $Ax + By + C = 0$,the values $L(x_1, y_1)$ and $L(x_2, y_2)$ must have the same sign,i.e.,$L(x_1, y_1) \times L(x_2, y_2) > 0$. For point $(1, 2)$,$L(1, 2) = 3(1) - 5(2) + a = a - 7$. For point $(3, 4)$,$L(3, 4) = 3(3) - 5(4) + a = a - 11$. Thus,we require $(a - 7)(a - 11) > 0$. This inequality holds when $a 11$.

Class 11 Mathematics Straight Line Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

Easy

Find the set of all values of $a$ such that both the points $(1, 2)$ and $(3, 4)$ lie on the same side of the line $3x - 5y + a = 0$.

AP EAMCET 2017 All AP EAMCET

A
$a > 11$
B
$a > 11 \cup a < 7$
C
$a < 7$
D
$\phi$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Line

Subtopic

Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

Previous Year

AP EAMCET 2017 Paper All AP EAMCET years →

If $\alpha = 1 + \sum_{r=1}^6 (-3)^{r-1} \binom{12}{2r-1}$,then the distance of the point $(12, \sqrt{3})$ from the line $\alpha x - \sqrt{3} y + 1 = 0$ is ..........

DifficultJEE MAIN 2025

View Solution

The length of the intercept of the line $x+1=0$ between the lines $3x+2y=5$ and $3x+2y=3$ is

EasyAP EAMCET 2022

View Solution

The length of the perpendicular from the point $(b, a)$ to the line $\frac{x}{a} - \frac{y}{b} = 1$ is:

Easy

View Solution

For the three points $A(2,0)$,$B(0,2)$,and $P(1,1)$,suppose $d$ is the algebraic sum of the distances of $A$ and $B$ from a line that passes through $P$. Then,which of the following is correct?

EasyAP EAMCET 2022

View Solution

The distance between two parallel lines $3x + 4y - 8 = 0$ and $3x + 4y - 3 = 0$ is given by

Easy

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

Find the set of all values of $a$ such that both the points $(1, 2)$ and $(3, 4)$ lie on the same side of the line $3x - 5y + a = 0$.

Similar Questions

If $\alpha = 1 + \sum_{r=1}^6 (-3)^{r-1} \binom{12}{2r-1}$,then the distance of the point $(12, \sqrt{3})$ from the line $\alpha x - \sqrt{3} y + 1 = 0$ is ..........

The length of the intercept of the line $x+1=0$ between the lines $3x+2y=5$ and $3x+2y=3$ is

The length of the perpendicular from the point $(b, a)$ to the line $\frac{x}{a} - \frac{y}{b} = 1$ is:

For the three points $A(2,0)$,$B(0,2)$,and $P(1,1)$,suppose $d$ is the algebraic sum of the distances of $A$ and $B$ from a line that passes through $P$. Then,which of the following is correct?

The distance between two parallel lines $3x + 4y - 8 = 0$ and $3x + 4y - 3 = 0$ is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module