Question:
Given that the slope of the tangent to a curve $\mathrm{y}=\mathrm{y}(\mathrm{x})$ at any point $(\mathrm{x}, \mathrm{y})$ is $\frac{2 \mathrm{y}}{\mathrm{x}^{2}}$. If the curve passes through the centre of the circle
$x^{2}+y^{2}-2 x-2 y=0$, then its equation is
$x \log _{e}|y|=2(x-1)$
$x \log _{e}|y|=x-1$
$x^{2} \log _{e}|y|=-2(x-1)$
$x \log _{e}|y|=-2(x-1)$
Correct Option: 1,
Solution:
$\operatorname{given} \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{2 \mathrm{y}}{\mathrm{x}^{2}}$
$\Rightarrow \int \frac{\mathrm{dy}}{2 \mathrm{y}}=\int \frac{\mathrm{dx}}{\mathrm{x}^{2}}$
$\Rightarrow \frac{1}{2} \ell \mathrm{ny}=-\frac{1}{\mathrm{x}}+\mathrm{c}$
passes through centre $(1,1)$
$\Rightarrow \mathrm{c}=1$
$\Rightarrow \mathrm{x} \ell \mathrm{ny}=2(\mathrm{x}-1)$
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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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