(B) Let the point on the line $x+y=4$ be $P(h, 4-h)$.The perpendicular distance from $P(h, 4-h)$ to the line $4x+3y-10=0$ is given by $d = \frac{|4h +

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

(B) Let the point on the line $x+y=4$ be $P(h, 4-h)$.The perpendicular distance from $P(h, 4-h)$ to the line $4x+3y-10=0$ is given by $d = \frac{|4h + 3(4-h) - 10|}{\sqrt{4^2 + 3^2}}$.Given $d=1$,we have $\frac{|4h + 12 - 3h - 10|}{5} = 1$.$|h + 2| = 5$.This gives two cases:Case $1$: $h+2 = 5 \implies h = 3$. The point is $(3, 4-3) = (3, 1)$.Case $2$: $h+2 = -5 \implies h = -7$. The point is $(-7, 4-(-7)) = (-7, 11)$.Thus,the coordinates are $(3, 1)$ and $(-7, 11)$.

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

Medium

The coordinates of the two points lying on $x+y=4$ and at a unit distance from the straight line $4x+3y=10$ are

WBJEE 2011 All WBJEE

A
$(-3,1), (7,11)$
B
$(3,1), (-7,11)$
C
$(3,1), (7,11)$
D
$(5,3), (-1,2)$

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

WBJEE 2011 Paper All WBJEE years →

Find the distance between the lines $5x + 12y + 13 = 0$ and $5x + 12y - 9 = 0$.

Easy

View Solution

If $(\sin \theta, \cos \theta)$ and $(3, 2)$ lie on the same side of the line $x + y = 1$,then $\theta$ lies in the interval:

Medium

View Solution

If the length of the perpendicular from the origin to the line $x/a + y/b = 1$ is $p$,then which of the following is true for $a^2, 4p^2, b^2$?

Medium

View Solution

Let the expression $E = 8^a + 8^b - 3 \cdot 2^{a+b}$ take its minimum value $p$ at $a = \alpha$ and $b = \beta$. Then,the perpendicular distance of the point $P(\alpha, \beta)$ from the line $x + y + 2p = 0$ is

View Solution

Lines are drawn parallel to the line $4x - 3y + 2 = 0$ at a distance of $\frac{3}{5}$ from the origin. Which one of the following points lies on any of these lines?

DifficultJEE MAIN 2019

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

The coordinates of the two points lying on $x+y=4$ and at a unit distance from the straight line $4x+3y=10$ are

Similar Questions

Find the distance between the lines $5x + 12y + 13 = 0$ and $5x + 12y - 9 = 0$.

If $(\sin \theta, \cos \theta)$ and $(3, 2)$ lie on the same side of the line $x + y = 1$,then $\theta$ lies in the interval:

If the length of the perpendicular from the origin to the line $x/a + y/b = 1$ is $p$,then which of the following is true for $a^2, 4p^2, b^2$?

Let the expression $E = 8^a + 8^b - 3 \cdot 2^{a+b}$ take its minimum value $p$ at $a = \alpha$ and $b = \beta$. Then,the perpendicular distance of the point $P(\alpha, \beta)$ from the line $x + y + 2p = 0$ is

Lines are drawn parallel to the line $4x - 3y + 2 = 0$ at a distance of $\frac{3}{5}$ from the origin. Which one of the following points lies on any of these lines?

Vedclass Test Series

Exam Paper Generator

Online Exam Module