Find the equation of a line whose inclination with the $x$-axis is $150^{\circ}$ and which passes through the point $(3,-5)$.
As angle is given so we have to find slope first give by m = tanθ
$m=\tan 150^{\circ}$
$\mathrm{m}=\tan \left(180^{\circ}-30^{\circ}\right) \Rightarrow-\tan 30^{\circ}=-\frac{1}{\sqrt{3}}\left(\tan \left(180^{\circ}-\theta\right)\right.$ is in II quadrant, $\tan x$ is negative)
Now the line is passing through the point $(3,-5)$. Using the slope - intercept form of the equation of the line, we will find the intercept
$y=m x+c$..................(1)
$-5=-\frac{1}{\sqrt{3}}(3)+\mathrm{c} \Rightarrow \mathrm{c}=-5+\sqrt{3}$
Putting the value of c in equation (1),we have
$y=-\frac{1}{\sqrt{3}} x+(-5+\sqrt{3})$
$x+(\sqrt{3}) y+5 \sqrt{3}-3=0$
So, required equation of line is $\mathrm{x}+(\sqrt{3}) \mathrm{y}+5 \sqrt{3}-3=0$.
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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,