Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.
The equation of line in intercept form is
$\frac{x}{a}+\frac{y}{b}=1$
Where $\mathrm{a}$ and $\mathrm{b}$ are the intercepts on the axis. Given that $\mathrm{a}+\mathrm{b}=14$
The above equation can be written as
$\Rightarrow \mathrm{b}=14-\mathrm{a}$
Substituting the value of $a$ and $b$ in equation 1 we get So, equation of line is
$\frac{x}{a}+\frac{y}{14-a}=1$
Taking LCM
$\Rightarrow \frac{x(14-a)+a y}{(a)(14-a)}=1$
$\Rightarrow 14 x-a x+a y=14 a-a^{2} \ldots \ldots 2$
$\Rightarrow \frac{x(14-a)+a y}{(a)(14-a)}=1$
$\Rightarrow 14 x-a x+a y=14 a-a^{2} \ldots \ldots .2$
$\Rightarrow \frac{x(14-a)+a y}{(a)(14-a)}=1$
$\Rightarrow 14 x-a x+a y=14 a-a^{2} \ldots \ldots 2$
If equation 2 passes through the point $(3,4)$ then
$14(3)-a(3)+a 4)=14 a-a^{2}$
$\Rightarrow 42-3 a+4 a-14 a+a^{2}=0$
$\Rightarrow a^{2}-13 a+42=0$
$\Rightarrow a^{2}-7 a-6 a+42=0$
$\Rightarrow a(a-7)-6(a-7)=0$
$\Rightarrow(a-6)(a-7)=0$
$\Rightarrow a-6=0$ or $a-7=0$
$\Rightarrow a=6$ or $a=7$
If $a=6$, then
$\Rightarrow b=14-6=8$
If $a=7$, then
$7+b=14$
$\Rightarrow b=14-7$
$=7$
If $a=6$ and $b=8$, then equation of line is
$\frac{x}{6}+\frac{y}{8}=1$
$\Rightarrow \frac{4 x+3 y}{24}=1$
$\Rightarrow 4 x+3 y=24$
If $a=7$ and $b=7$, then equation of line is
$\frac{x}{7}+\frac{y}{7}=1$
$\Rightarrow x+y=7$
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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,