Question:
Find a point on the x-axis which is equidistant from the points A (7, 6) and B(- 3, 4).
Solution:
Let the point on x-axis be P(x, 0).
Given: Point $P(x, 0)$ is equidistant from points $A(7,6)$ and $B(-3,4)$
i.e., distance of $P$ from $A=$ distance of $P$ from $B$
$\Rightarrow \sqrt{(x-7)^{2}+36}=\sqrt{(x+3)^{2}+16}$
Squaring both sides,
$\Rightarrow(x-7)^{2}+36=(x+3)^{2}+16$
$\Rightarrow x^{2}-14 x+49+36=x^{2}+6 x+9+16$
$\Rightarrow-20 x=-60$
$\Rightarrow x=3$
Therefore, the point on the x-axis is (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,
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