Question:
The tangent and normal to the ellipse $3 x^{2}+5 y^{2}=32$ at the point $P(2,2)$ meet the $x$-axis at $Q$ and $R$, respectively. Then the area (in sq. units) of the triangle $P Q R$ is :
$\frac{14}{3}$
$\frac{16}{3}$
$\frac{68}{15}$
$\frac{34}{15}$
Correct Option: , 3
Solution:
$3 x^{2}+5 y^{2}=32$
$\left.\frac{\mathrm{dy}}{\mathrm{dx}}\right|_{(2,2)}=-\frac{3}{5}$
Tangent : $\mathrm{y}-2=-\frac{3}{5}(\mathrm{x}-2) \Rightarrow \mathrm{Q}\left(\frac{16}{3}, 0\right)$
Normal : $\mathrm{y}-2=\frac{5}{3}(\mathrm{x}-2) \Rightarrow \mathrm{R}\left(\frac{4}{5}, 0\right)$
Area is $=\frac{1}{2}(\mathrm{QR}) \times 2=\mathrm{QR}=\frac{68}{15}$
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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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