Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :
$24 x^{2}-25 y^{2}=600$
Given Equation: $24 x^{2}-25 y^{2}=600 \Rightarrow$
$\frac{x^{2}}{25}-\frac{y^{2}}{24}=1$
Comparing with the equation of hyperbola
$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ we get,
$a=5$ and $b=\sqrt{24}=2 \sqrt{6}$
(i) Length of Transverse axis $=2 a=10$ units.
Length of Conjugate axis $=2 b=4 \sqrt{6}$ units.
(ii) Coordinates of the vertices $=(\pm a, 0)=(\pm 5,0)$
(iv) Here, eccentricity, $e=\sqrt{1+\frac{b^{2}}{a^{2}}}=\sqrt{1+\frac{24}{25}}=\sqrt{\frac{49}{25}}=\frac{7}{5}$
(iii) Coordinates of the foci $=(\pm a e, 0)=(\pm 7,0)$
(v) Length of the rectum $=\frac{2 b^{2}}{a}=\frac{48}{5}=9.6$ units.
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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,