Find the equation of the circle passing through the point $(-1,-3)$ and having its centre at the point of intersection of the lines $x-2 y=4$ and $2 x+5 y+1$ $=0$.
The intersection of the lines: $x-2 y=4$ and $2 x+5 y+1=0$.
is $(2,-1)$
$\therefore$ This problem is same as solving a circle equation with centre and point on the circle given.
The general form of the equation of a circle is:
$(x-h)^{2}+(y-k)^{2}=r^{2}$
Where, (h, k) is the centre of the circle.
r is the radius of the circle.
In this question we know that $(h, k)=(2,-1)$, so for determining the equation of the circle we need to determine the radius of the circle.
Since the circle passes through $(-1,-3)$, that pair of values for $x$ and $y$ must satisfy the equation and we have:
$\Rightarrow(-1-2)^{2}+(-3-(-1))^{2}=r^{2}$
$\Rightarrow(-3)^{2}+(-2)^{2}=r^{2}$
$\Rightarrow r^{2}=9+4=13$
$\therefore r^{2}=13$
⇒ Equation of circle is:
$(x-2)^{2}+(y-(-1))^{2}=13$
$\Rightarrow(x-2)^{2}+(y+1)^{2}=13$
Ans: $(x-2)^{2}+(y+1)^{2}=13$
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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,