RS Aggarwal Class 11 Chapter 21 Solutions (Circles)
RS Aggarwal Class 11 Chapter 21 Circles is introduced to give detailed information on the Chapter Circles. This book is one of the famous reference books that you should refer to if you are preparing for your CBSE exams or other competitive exams. RS Aggarwal Solutions for Class 11 Chapter 21 is going to be your best companion as this book presents you detailed solutions according to the latest exam patterns.
This Chapter discusses different topics like the equation of a circle in standard form, equation of a circle, the endpoints of whose diameter are given, the general equation of a circle, etc. The Chapter has only two exercises with a total of 17 questions. These questions cover all the topics of the Chapter and help you in building a strong base regarding Chapter Circles.
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Topics covered under Class 11 Chapter 21 Circles
Circle: A circle is known as the set of all points in a plane that remains at a constant distance from a fixed point in a plane.
The fixed point on a plane in a circle is called the center and the constant distance from the center of the circle is called the radius of the circle.
Important Points to remember:
- if r(r > 0) is the radius of a circle and the diameter d = 2r is the maximum distance between any two points on the given Circles.
- The length of the curve or perimeter (also called the circumference) of circle
- The area of a circle
- The line joining any two points of a circle is called the chord of a circle.
- The curved section between any two points of a circle is called the arc of the circle.
- The angle subtended at the center of a circle by any arc = arc/radius.
- Angles subtended at the center of a circle and arc are double or subtended at the circumference of a circle.
Equation of a circle in standard form
The equation of a circle with center (h,k) and radius r is given by (x-h)2 + (y-k)2 = r2
The equation of a circle with center at the origin and radius r is given by x2 + y2 = r2.
Equation of a circle, the endpoints of whose diameter are given
Theorem 3: The equation of a circle described on the line joining A(x1, y1) and B (x2 y2) as the diameter is (x – x1)(x – x2) + (y – y2)(y – y2) = 0.
General Equation Of a Circle
Theorem: The general equation of a circle is of the form x2 + y2 + 2gx + 2fy + c = 0.
Also, every equation of form x2 + y2 + 2gx + 2fy + c = 0 represents a circle if (g2 + f2 – c) >0.
- The general equation of a second degree ax2 + by2 + 2hxy + 2gx + 2fy + c = 0 represents a circle if a = b ≠ 0 and h = 0.
- Locus of a point p represents a circle if its distance from two points A and B are not equal i.e. PA = kPB represents a circle if k ≠ 1.
- Discussion on nature of the circle :
- If g2 + f2 – c > 0, then the radius of the circle will be real. Hence, in this case, it is possible to draw a circle on a plane.
- If g2 + f2 – c = 0, then the radius of the circle will be zero. Such a circle is known as a point circle.
Exercise Wise Discussion Of Chapter 21 Circles
The Chapter has two exercises with a total of 17 questions. All these questions cover the topic of the Chapter and help you in preparing well for your exams.
- Exercise 21A
This exercise 21A has 8 Questions in which you have to find equations of Circles given its center and radius.
- Exercise 21B
This exercise 21B has 9 Questions in which you have to find the equation of the circle in different situations. Exercise 21B is a bit difficult and needs a clear understanding of the concepts to solve the questions.
Benefits of RS Aggarwal Class 11 Chapter 12 By Instasolv
Instasolv has been a proficient team in serving the students with the best solutions. No matter whatever the topic or the Chapter you face issues with, we at Instasolv will give you the easy to understand solutions. It is essential for you to understand all concepts properly as Class 11 is the base of Class 12.
In order to score well in the RS Aggarwal Class 11 Maths Solutions CBSE exams, it is crucial to learn the concepts in Class 11 so that you can score well in both Classes. After all, you will join college after Class 12.