If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154square units, then obtain the equation of the circle.
Since, diameters of a circle intersect at the centre of a circle,
2x – 3y = 5 ………1
3x – 4y = 7 ………..2
Solving the above equations,
Multiplying equation 1 by 3 we get
6x – 9y = 15
Multiplying equation 2 by 2 we get
6x – 8y = 14
y = 1
y = -1
Putting y = -1, in equation 1, we get
2x – 3(-1) = 5
2x + 3 = 5
2x = 2
x = 1
Coordinates of centre = (1,-1)
Given area = 154
Area = πr2 = 154
22/7 × r2 = 154
r2 = 154 × 7/22
r = 7 units
Since, the equation of a circle having centre (h, k), having radius as r units, is
(x – h)2 + (y – k)2 = r2
(x – 1)2 + (y – (-1))2 = 72
x2 – 2x +1 + (y + 1)2 = 49
x2 – 2x + 1 + y2 + 2y + 1 – 49 = 0
x2 – 2x + y2 + 2y – 47 = 0
Hence the required equation of the given circle is x2 – 2x + y2 + 2y – 47 = 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,