Question:
If the circles $x^{2}+y^{2}+5 K x+2 y+K=0$ and $2\left(x^{2}+y^{2}\right)+2 K x+3 y-1=0,(K \in R)$, intersect at the points $\mathrm{P}$ and $\mathrm{Q}$, then the line $4 x+5 y-K=0$ passes through $P$ and $Q$ for :
exactly two values of K
exactly one value of K
no value of K.
infinitely many values of K
Correct Option: , 3
Solution:
Equation of common chord
$4 \mathrm{kx}+\frac{1}{2} \mathrm{y}+\mathrm{k}+\frac{1}{2}=0$ .....(1)
and given line is $4 x+5 y-k=0$ .......(2)
On comparing (1) & (2), we get
$k=\frac{1}{10}=\frac{k+\frac{1}{2}}{-k}$
$\Rightarrow$ No real value of $k$ exist
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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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