Question:
Find the equation of the tangent line to the curve $y=x^{2}+4 x-16$ which is parallel to the line $3 x-y+1=0$.
Solution:
finding the slope of the tangent by differentiating the curve
$\frac{d y}{d x}=2 x+4$
$m($ tangent $)=2 x+4$
equation of tangent is given by $y-y_{1}=m($ tangent $)\left(x-x_{1}\right)$
now comparing the slope of a tangent with the given equation
$2 x+4=3$
$x=-\frac{1}{2}$
Now substituting the value of $x$ in the curve to find $y$
$y=\frac{1}{4}-2-16=-\frac{71}{4}$
Therefore, the equation of tangent parallel to the given line is
$y+\frac{71}{4}=3\left(x+\frac{1}{2}\right)$
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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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- Chemical Effects of Electric Current,
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