Find The Equation Of The Circle Which Passes Through The Origin And Belongs To The Co-axial Of Circles Whose Limiting Points Are (1, 2) And (4, 3).

  1. Home
  2. JEE Main
  3. Maths
  4. Coordinate Geometry
  5. Coordinate Systems and Coordinates

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

Question

Find the equation of the circle which passes through the origin and belongs to the co-axial of circles whose limiting points are (1, 2) and (4, 3).

Solution

Correct option is

2x2 + 2y2 – x – 7y = 0

 

Equations of circles whose limiting points are (1, 2) and (4, 3) are

                     (x – 1)2 + (y – 2)2 = 0 

or               x2 + y2 – 2x – 4y + 5 = 0                      …(1)

and               (x – 4)2 + (y – 3)2 = 0

or              x2 + y2 – 8x – 6y + 25 = 0                     …(2)

Therefore the corresponding system of co-axial circle is

    (x2 + y2 – 2x – 4y + 5) + λ(x2 + y2 – 8x – 6y + 25) = 0       …(3)

It passes through origin then

                      5 + 25λ = 0

  

Substituting the value of λ in (3), the required circle is

        5(x2 + y2 – 2x – 4y + 5) – (x2 + y2 – 8x – 6y + 25) = 0

or     4x2 + 4y2 – 2x – 14y = 0

or     2x2 + 2y2 – x – 7y = 0

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

SIMILAR QUESTIONS

Q1

Find the circle whose diameter is the common chord of the circles x2 + y2+ 2x + 3y + 1 = 0 and x2 + y2 + 4x + 3y + 2 = 0.
medium View solution
Q2

 

Find the angle between the circles
easy View solution
Q3

Find the equation of the circle which cuts the circle x2 + y2 + 5x + 7y – 4 = 0 orthogonally, has its centre on the line x = 2 and passes through the point (4, –1).
medium View solution
Q4

 

Find the equations of the two circles which intersect the circles

        x2 + y2 – 6y + 1 = 0 and x2 + y2 – 4y + 1 = 0  

Orthogonally and touch the line 3x + 4y + 5 = 0.   
diffcult View solution
Q5

 

Find the radical centre of circles x2 + y2 + 3x + 2y + 1 = 0,

x2 + y2 – x + 6y + 5 = 0 and x2 + y2 + 5x – 8y + 15 = 0. Also find the equation of the circle cutting them orthogonally.
medium View solution
Q6

Find the radical centre of three circles described on the three sides 4x – 7y + 10 = 0, x + y – 5 = 0 and 7x + 4y – 15 = 0 of a triangle as diameters.
easy View solution
Q7

 

Find the co-ordinates of the limiting points of the system of circles determined by the two circles

  x2 + y2 + 5x + y + 4 = 0 and x2 + y2 + 10x – 4y – 1 = 0      
diffcult View solution
Q8

If the origin be one limiting point of a system of co-axial circles of whichx2 + y2 + 3x + 4y + 25 = 0 is a member, find the other limiting point.
medium View solution
Q9

Find the radical axis of co-axial system of circles whose limiting points are (–1, 2) and (2, 3).
easy View solution
Q10

Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.
easy View solution