Question:
Find the equation of the normal to the curve $a y^{2}=x^{3}$ at the point $\left(a m^{2}, a m^{3}\right)$.
Solution:
finding the slope of the tangent by differentiating the curve
$2 a y \frac{d y}{d x}=3 x^{2}$
$\frac{d y}{d x}=\frac{3 x^{2}}{2 a y}$
$\mathrm{m}$ (tangent) at $\left(\mathrm{am}^{2}, \mathrm{am}^{3}\right)$ is $\frac{3 \mathrm{~m}}{2}$
normal is perpendicular to tangent so, $m_{1} m_{2}=-1$
$\mathrm{m}$ (normal) at $\left(\mathrm{am}^{2}, \mathrm{am}^{3}\right)$ is $-\frac{2}{3 \mathrm{~m}}$
equation of normal is given by $y-y_{1}=m($ normal $)\left(x-x_{1}\right)$
$y-a m^{3}=-\frac{2}{3 m}\left(x-a m^{2}\right)$
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- 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
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- Chemical Effects of Electric Current,
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