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S.L. Loney System of Circles Solutions (Chapter 9)

SL Loney Elements of Coordinate Geometry Solutions Chapter 9 illustrates the concepts related to the systems of circles. These solutions provided by Instasolv consists of answers to all the important questions which are found in the SL Loney Solutions textbook and those questions that are common in the competitive exams like JEE Mains, JEE Advanced, and NEET. Practice well to score good marks in the exams.

The main topics of this SL Loney Chapter 9 Solutions System of Circles include orthogonal circles, the radical axis of two circles, geometrical construction, coaxal circles, limiting points of a coaxial system, orthogonal circles of a coaxial system, and more. Referring to these SL Loney Elements of Coordinate Geometry Solutions will help you understand the topics of the system of circles more clearly. 

In this chapter of the SL Loney System of Circles Solutions, there are 2 different exercises with a total of 31 questions available to practice. This includes short answer type questions and long answer type questions. The solutions to these various questions have been prepared by our expert Maths teachers and will help you to understand the concepts of the chapter in a better way. Follow these solutions provided by Instasolv now for free.

Important Topics for SL Loney Elements of Coordinate Geometry Solutions Chapter 9: System of Circles

The main concepts of the SL Loney System of Circles Solutions are explained well below. Refer to these important topics provided by the experts of Instasolv to make your concepts stronger.

Circle

A circle refers to a figure consisting of all points in a surface that are a provided distance from a specified point, the centre; consistently it is the curve drawn out by a point that moves in a surface so that its location from a given point is continuous.

Systems of Circles

If each and every pair of circles from the system has the equivalent radical axis then the coaxial is in the system of circles. Thus, a coaxial system of circles is being defined with the help of the radical axis and by anyone of the circle.

Radical Axis of Two Circles

The line through which the two circles are at a 90-degree angle to the line linking the centres of the circle is said to be the radical axis of two non-concentric circles. The radical axis is the line through which the circle crosses their two crossing points, and it is their line of tangency if they are tangent.

Radical Centre

The radical center is known as the power center of three circles. These circles refer to the three radical axes intersecting at a point of the pairs of circles. If the radical center is located outside of all three circles, then it is the center of the exclusive circle that interconnects the three specified circles orthogonally whereas the creation of this orthogonal circle resembles Monge’s problem.

Coaxal Circles

Coaxal circles refer to those circles that share a mutual radical line and whose centres are collinear with one another. A pencil of coaxal circles refers to the collection of all coaxal circles.

Equation of a System of Coaxal Circles

The system of coaxal circles is defined if each and every pair of the system has the equivalent radical axis. A coaxial system is formed by the circles passing through two fixed points.

The equation that shows a family of the coaxial circles is:

S+λp =0, S1+ λS2=0

Limiting Points of a Coaxal System

The limiting points of a coaxal system are a point by which inversion of two circles forms concentric circles. Each and every pair of distinct circles has two limiting points.

Orthogonal Circles

Two circles are said to be orthogonal if they intersect at 90-degrees at each intersection.

Exercise-wise Discussion for SL Loney Elements of Coordinate Geometry Solutions Chapter 9: System of Circles

The solutions of SL Loney Coordinate Geometry Chapter 9 consists of 2 main exercises with a total of 31 questions in the chapter. The detailed description of all these exercises are listed below:

Exercise 1 – Short Answer Type Questions

In this exercise of Chapter 9 ‘System of Circle’, there are a total of 16 questions that are based on the concepts of orthogonal circles, the radical axis of two circles, and geometrical construction. Practice well to have a better understanding of the chapter.

Exercise 2 – Long Answer Type Questions

Exercise 2 of SL Loney Chapter 9 Solutions contains a total of 15 questions. They are long answer type questions based on coaxal circles, limiting points of a coaxial system, and orthogonal circles of a coaxial system. Practice the exercise well to score good marks in your competitive exams like JEE and NEET.

Why Use SL Loney Elements of Coordinate Geometry Solutions Chapter 9: System of Circles by Instasolv?

The main benefits of referring to the SL Loney Elements of Coordinate Geometry Solutions Chapter 9 System of Circles are listed below:

  • SL Loney Solutions are meticulously designed and specified for you by the team of experts at Instasolv.
  • These SL Loney System of Circles Solutions are meant to help you attain accurate answers to the many questions that arise and especially if you are not able to find such answers easily.
  • Referring to these solutions provided by Instasolv paves the way for you to grasp the important concepts and to thoroughly assess your abilities to understand the chapter in-depth.
  • You can refer to these solutions of Chapter 9 ‘System of Circles’ that we have handy for you as and when you have any difficulty in solving the questions from your textbooks.
  • It can be elaborated that these materials are a perfect support guide for you to score well in your CBSE exams as well as the competitive exams like IIT JEE and NEET.