Find the point on the curve $\frac{\mathrm{x}^{2}}{9}+\frac{\mathrm{y}^{2}}{16}=1$ at which the tangents are parallel to $\mathrm{x}$ - axis
Given:
The curve is $\frac{\mathrm{x}^{2}}{9}+\frac{\mathrm{y}^{2}}{16}=1$
Differentiating the above w.r.t $x$, we get the Slope of tangent,
$\Rightarrow \frac{2 x^{2-1}}{9}+\frac{2 y^{2-1} \times \frac{d y}{d s}}{16}=0$
$\Rightarrow \frac{2 x}{9}+\frac{y \times \frac{d y}{d x}}{8}=0$
Cross multiplying we get,
$\Rightarrow \frac{(8 \times 2 x)+(9 \times y) \times \frac{d y}{d x}=0}{72}$
$\Rightarrow 16 x+9 y \frac{d y}{d x}=0$
$\Rightarrow 9 y \frac{d y}{d x}=-16 x$
$\Rightarrow \frac{d y}{d x}=\frac{-16 x}{9 y} \ldots(1)$
(i)
Since, the tangent is parallel to $\mathrm{x}$ - axis]
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\tan (0)=0 \ldots(2)$
$\therefore \tan (0)=0$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}}=$ The Slope of the tangent $=\tan \theta$
From (1) \& (2), we get,
$\Rightarrow \frac{-16 x}{9 y}=0$
$\Rightarrow-16 x=0$
$\Rightarrow x=0$
Substituting $x=0$ in $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$
$\Rightarrow \frac{0^{2}}{9}+\frac{y^{2}}{16}=1$
$\Rightarrow y^{2}=16$
$\Rightarrow y=\pm 4$
Thus, the required point is $(0,4) \&(0,-4)$
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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,