P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is $\frac{x}{a}+\frac{y}{b}=2$
Let AB be the line segment between the axes and let P (a, b) be its mid-point.
Let the coordinates of A and B be (0, y) and (x, 0) respectively.
Since P (a, b) is the mid-point of AB,
$\left(\frac{0+x}{2}, \frac{y+0}{2}\right)=(a, b)$
$\Rightarrow\left(\frac{x}{2}, \frac{y}{2}\right)=(a, b)$
$\Rightarrow \frac{x}{2}=a$ and $\frac{y}{2}=b$
$\therefore x=2 a$ and $y=2 b$
Thus, the respective coordinates of A and B are (0, 2b) and (2a, 0).
The equation of the line passing through points (0, 2b) and (2a, 0) is
$(y-2 b)=\frac{(0-2 b)}{(2 a-0)}(x-0)$
$y-2 b=\frac{-2 b}{2 a}(x)$
$a(y-2 b)=-b x$
i.e., $b x+a y=2 a b$
On dividing both sides by ab, we obtain
$\frac{b x}{a b}+\frac{a y}{a b}=\frac{2 a b}{a b}$
$\Rightarrow \frac{x}{a}+\frac{y}{b}=2$
Thus, the equation of the line is $\frac{x}{a}+\frac{y}{b}=2$.
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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,