Question:
The slope of the tangent to the curve $x=3 t^{2}+1, y=t^{3}-1$ at $x=1$ is
A. $\frac{1}{2}$
B. 0
C. $-2$
D. $\infty$
Solution:
Given that $x=3 t^{2}+1, y=t^{3}-1$
For $x=1$
$3 t^{2}+1=1$
$\Rightarrow 3 t^{2}=0$
$\Rightarrow t=0$
Now, differentiating both the equations w.r.t. t, we get
$\frac{\mathrm{dx}}{\mathrm{dt}}=6 \mathrm{t}$ and $\frac{\mathrm{dy}}{\mathrm{dt}}=3 \mathrm{t}^{2}$
$\Rightarrow$ Slope of the curve:
$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$
$=\frac{3 t^{2}}{6 t}$
$=\frac{1}{2} t$
For $t=0$,
Slope of the curve $=0$
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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