Question:
Write the coordinates of the point on the curve $y^{2}=x$ where the tangent line makes an angle $\frac{\pi}{4}$ with $x$-axis.
Solution:
Given that the curve $y^{2}=x$ has a point where the tangent line makes an angle $\frac{\pi}{4}$ with $x$-axis.
$\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\tan 45^{\circ}=1$
$\because$ the point lies on the curve.
$y^{2}=x$
$\Rightarrow 2 y \frac{d y}{d x}=1$
$\Rightarrow \frac{d y}{d x}=\frac{1}{2 y}$
$\Rightarrow \frac{1}{2 y}=1$
$\Rightarrow y=\frac{1}{2}$
So, $\mathrm{x}=\frac{1}{4}$
Hence, the required point is $\left(\frac{1}{4}, \frac{1}{2}\right)$
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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
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- Dual Nature of Radiation and Matter
- Atoms
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- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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