Find the equations of all lines having slope 0 which are tangent to the curve $y=\frac{1}{x^{2}-2 x+3}$.
The equation of the given curve is $y=\frac{1}{x^{2}-2 x+3}$.
The slope of the tangent to the given curve at any point (x, y) is given by,
$\frac{d y}{d x}=\frac{-(2 x-2)}{\left(x^{2}-2 x+3\right)^{2}}=\frac{-2(x-1)}{\left(x^{2}-2 x+3\right)^{2}}$
If the slope of the tangent is 0, then we have:
$\frac{-2(x-1)}{\left(x^{2}-2 x+3\right)^{2}}=0$
$\Rightarrow-2(x-1)=0$
$\Rightarrow x=1$
When $x=1, y=\frac{1}{1-2+3}=\frac{1}{2}$
$\therefore$ The equation of the tangent through $\left(1, \frac{1}{2}\right)$ is given by,
$y-\frac{1}{2}=0(x-1)$
$\Rightarrow y-\frac{1}{2}=0$
$\Rightarrow y=\frac{1}{2}$
Hence, the equation of the required line is $y=\frac{1}{2}$.
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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,