Question:
The equation of tangent at those points where the curve $y=x^{2}-3 x+2$ meets $x$-axis are
A. $x-y+2=0=x-y-1$
B. $x+y-1=0=x-y-2$
C. $x-y-1=0=x-y$
D. $x-y=0=x+y$
Solution:
Given that the curve $y=x^{2}-3 x+2$
$\Rightarrow \frac{d y}{d x}=2 x-3$
The tangent passes through point $(x, 0)$
$\Rightarrow 0=x^{2}-3 x+2$
$\Rightarrow(x-2)(x-1)=0$
$\Rightarrow x=1$ or 2
Equation of the tangent:
$\left(y-y_{1}\right)=$ Slope of tangent $x\left(x-x_{1}\right)$
Case: 1
When $x=2$
Slope of tangent $=1$
Equation of tangent:
$y=1 \times(x-2)$
$\Rightarrow x-y-2=0$
Case: 2
When $x=1$
Slope of tangent $=-1$
Equation of tangent:
$y=-1 \times(x-1)$
$\Rightarrow x+y-1=0$
Hence, option B is correct.
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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
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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