What are the points on the x-axis whose perpendicular distance from the line $\frac{x}{3}+\frac{y}{4}=1$ is 4 units?
Given: perpendicular distance is 4 units and line
$\frac{x}{3}+\frac{y}{4}=1$
To find : points on the x-axis
Formula used:
We know that the length of the perpendicular from (m,n) to the line ax + by + c = 0 is given by,
$D=\frac{|a m+b n+c|}{\sqrt{a^{2}+b^{2}}}$
The equation of the line is $4 x+3 y-12=0$
Any point on the $x$-axis is given by $(x, 0)$
Here $m=x$ and $n=0, a=4, b=3, c=-12$ and $D=4$ units
$D=\frac{|4(x)+3(0)-12|}{\sqrt{4^{2}+3^{2}}}=4$
$D=\frac{|4 x-12|}{\sqrt{16+9}}=\frac{|4 x-12|}{\sqrt{25}}=\frac{|4 x-12|}{5}=4$
$|4 x-12|=4 \times 5=20$
$4 x-12=20$ or $4 x-12=-20$
$4 x=20+12$ or $4 x=-20+12$
$4 x=32$ or $4 x=-8$
$x=32 / 4=8$ or $x=(-8) / 4=-2$
(8,0) and (2,0)are the points on the x-axis whose perpendicular distance from the line is 4 units
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,