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S.L. Loney The Circle Solutions (Chapter 8)

SL Loney Elements of Coordinate Geometry Solutions Chapter 8 ‘The Circle’ helps you understand the concepts of the chapter in-depth. All these SL Loney The Circle Solutions are prepared by expert teachers of Maths who understand the parameters and guidelines set by CBSE for SL Loney Coordinate Geometry Solutions. These solutions are also ideal study material for JEE and NEET preparation. The solutions contain detailed explanations of all the questions given. 

The Circle is an important chapter to understand the different concepts of coordinate geometry like the general equation of a circle, the tangent of a circle, the circumference of a circle, equation to the tangent of a circle, the intersection of a straight line and a circle, and equation to any tangent. Referring to these solutions, you will also study the normal to the circle, pole and polar, chord of contact of a tangent, geometrical construction for the polar, pair of tangents from any point, polar equation to the circle, polar equation to the tangent, and oblique coordinates.

Chapter 8 ‘The Circle’ of SL Loney Elements of Coordinate Geometry consists of a total of 6 exercises with 133 questions. Our experts have provided stepwise solutions to each exercise question to ensure your complete clarity on the concepts. The SL Loney The Circle Solutions will help you to understand the chapter as well as remember it in a way that you can answer any question and score well. Follow the solutions provided by Instasolv now for free.

Important Topics for SL Loney Elements of Coordinate Geometry Solutions Chapter 8: The Circle

The Circle

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

The Radius of a Circle

The radius of a circle is defined as a line from the centre of the circle to some extent on the side. The letter r is used for the length of a circle’s radius. The centre of a circle is the point within the very middle.

Tangents to a Circle 

Tangents to a circle are defined as the lines that meet the circle closes in one single point. The point where the circle is being touched by the tangent is called the point of tangency. The tangent is at a 90-degree angle to the radius at the point of tangency.

Properties of Tangents of a Circle:

The properties of the tangent of a circle are listed below:

  • The tangent line only touches the circle, never crosses it.
  • At the point of tangency, the radius and the tangent are perpendicular to each other.
  • The tangent and the chord always form an angle and this angle is the same as that of a tangent inscribed on the other side of the chord.
  • The tangent segments to a circle are always equal from the same external point.

A Straight line Intersection to a Circle

The line always intersects the circle at two different points if the distance among the radius is less. The line will always touch the circle if the distance among the radius is equivalent. Similarly, the line will lie completely outside the circle if the distance among the radius is more.

Chord of a Circle

The line segment joining any two points of a circle is known as a chord. The endpoints of the line segments placed on the circumference of the circle. Diameter is the chord that passes through the middle of the circle. It’s the longest chord possible during a circle.

Chord of Contact

The chord of contact is a chord that joins the points of contact of the two tangents from the outside of the conic drawn or from a given point. 

Pole and Polar of a circle

If X and Y are the tangents to the circle meeting at O, then the locus of O is known as the polar of P with respect to the circle and P is known as the pole. If X and Y are the tangents to the circle meeting at O, then the straight line OO is called the polar of P, and P is referred to as the pole.

General Equation of a Circle

The equation of a circle is classified into two types including the general form and the standard form. One can easily find the radius and the centre of the circle if the equation of a circle is in the standard form. The radius is always positive in the standard form. 

Exercise-wise Discussion for SL Loney Elements of Coordinate Geometry Solutions Chapter 8: The Circle

SL Loney Elements of Coordinate Geometry Chapter 8 consists of a total of 6 exercises with 133 questions. The brief description of all the exercises is provided below:

Exercise 1 – Very Short Answer Type Questions

This exercise of SL Loney Solutions for Chapter 8 has around 36 questions which are short answer type questions. These questions are based on the general equation of a circle.

Exercise 2 – Short Answer Type Questions

Exercise 2 consists of 22 questions that are short answer type questions based on the equation to the tangent, intersection of a straight line and a circle, equation to any tangent, and the normal to the circle. Practising these questions will help you clear your concepts.

Exercise 3 – Long Answer Type Questions

Exercise 3 contains a total of 23 questions. It consists of long answer type questions for your practice. All the questions of this exercise are based on the important concepts of pole and polar, the chord of contact of a tangent, and geometrical construction for the polar.

Exercise 4, 5, and 6 have a total of 8, 8, and 36 questions respectively. These exercises are based on the concepts of pairs of tangents from any point, polar equation to the circle, polar equation to the tangent, and oblique coordinates. All these exercises are considered important from the entrance exams point of view. So, practice well to score good marks in your exams.

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