Question:
Write the equation of the tangent to the curve $y=x^{2}-x+2$ at the point where it crosses the $y$-axis.
Solution:
Given that the curve $y=x^{2}-x+2$ has a point crosses the $y$-axis.
The curve will be in the form of $(0, y)$
$\Rightarrow y=0-0+2$
$\Rightarrow y=2$
So, the point at which curve crosses the $y$-axis is $(0,2)$.
Now, differentiating the equation of curve w.r.t. $x$
$\frac{d y}{d x}=x-1$
For $(0,2)$,
$\frac{\mathrm{dy}}{\mathrm{dx}}=-1$
Equation of the tangent:
$\left(\mathrm{y}-\mathrm{y}_{1}\right)=$ Slope of tangent $\times\left(\mathrm{x}-\mathrm{x}_{1}\right)$
$\Rightarrow(y-2)=-1 \times(x-0)$
$\Rightarrow y-2=-x$
$\Rightarrow x+y=2$
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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,
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