Question:
Let $P$ be the point of intersection of the common tangents to the parabola $\mathrm{y}^{2}=12 \mathrm{x}$ and the hyperbola $8 x^{2}-y^{2}=8$. If $S$ and $S^{\prime}$ denote the foci of the hyperbola where $S$ lies on the positive $x$-axis then $P$ divides $\mathrm{SS}^{\prime}$ in a ratio:
$5: 4$
$14: 13$
$2: 1$
$13: 11$
Correct Option: 1
Solution:
Equation of tangents
$\mathrm{y}^{2}=12 \mathrm{x} \quad \Rightarrow \mathrm{y}=2 \mathrm{x}+\frac{3}{\mathrm{~m}}$
$\frac{x^{2}}{1}-\frac{y^{2}}{8}=1 \Rightarrow y=m x \pm \sqrt{m^{2}-8}$
Since they are common tangent
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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
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- Atoms
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