Question:
If the eccentricity of the standard hyperbola passing through the point $(4,6)$ is 2 , then the equation of the tangent to the hyperbola at $(4,6)$ is-
$2 x-y-2=0$
$3 x-2 y=0$
$2 x-3 y+10=0$
$x-2 y+8=0$
Correct Option: 1
Solution:
Let us Suppose equation of hyperbola is
$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$
$\mathrm{e}=2 \Rightarrow \mathrm{b}^{2}=3 \mathrm{a}^{2}$
passing through $(4,6) \Rightarrow \mathrm{a}^{2}=4, \mathrm{~b}^{2}=12$
$\Rightarrow$ equaiton of tangent
$x-\frac{y}{2}=1$
$\Rightarrow 2 x-y-2=0$
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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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