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Concise Mathematics Class 10 ICSE Solutions for Chapter 16 - Loci (Locus and Its Constructions)

## ICSE Class 10 Mathematics Chapter 16 Selina Concise Solutions - Free PDF Download

The Selina Solutions For Class 10 Maths Chapter 16 “Locus and its Construction” is a one-stop solution to all the doubts and queries on the sums covered in this topic. Students of class 10 are suggested to refer to these Selina Solutions and practice them for a better understanding of the concepts so they can score good marks in the examination. Students can download the Selina Solutions For Class 10 Maths Chapter 16 “Locus and its Construction” PDF from the link given below, for free.

Chapter 16 Locus and its Constructions explains the concepts of locus and various related topics that are important from the exam perspective. Several types of loci and their constructions are given in exercise 16 (B) of the Selina textbook for Class 10 Maths. The solutions that are given for exercise 16 (A), and 16 (B) will help the students to prepare for their board examination and other competitive examinations.

### Selina Mathematics Solutions Class 10 Chapter 16 - PDF

An attempt has been made to make the Selina Solution Class 10 Chapter 16 user friendly, thus minimizing the stress of students and providing easy access to the Selina solutions. The purpose to present these concepts, theories, examples, and solved exercises in a logical and interesting manner is to help all students to develop an interest in learning and understanding this topic.

Selina Solutions Class 10 Chapter 16 “Locus and its Constructions” has been prepared and consolidated as per the latest ICSE syllabus and guidelines. By referring to these solutions, students will be able to meet their objectives for the exam preparation.

### Locus

In Geometry, the locus is a set of points that satisfies a given situation or condition for a geometrical shape or figure. The plural form of the locus is known as loci. The area of the loci is referred to as the region. The term “ locus” is derived from the word location. Before the 20th century, geometrical shapes were determined as an entity or region where the points can be easily moved or located. However, in modern Mathematics, entities are determined as the collection of points that satisfy the given condition.

### Locus Meaning

A locus is a set of points that agrees to certain geometric situations or conditions. Most of the geometric shapes can be naturally described as loci of certain points. For example, a circle is a collection of points in a plane that are placed at a fixed distance r from a given point P, the center of the circle.

Problems on describing a specific locus can be explicitly solved by determining equations for the coordinates of the point in the locus. Here are some of the steps for determining plane loci.

Step 1: If possible, choose a coordinate system that makes the calculation and equations as simple as possible.

Step 2: Specify the given condition in the Mathematical form that involves the coordinates x and y.

Step 3: Rationalise the resulting equations.

Step 4: Recognise the shape carved out from a circle.

### Some Important Locus Theorem

The locus of a point that is spaced equally from two given intersecting lines is the bisector of the angle formed through the lines.

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The locus of a point that is spaced equally from two given points such as A and B is perpendicular to the line segment joining two points A and B.

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The locus of a point that is spaced equally from two given parallel lines is the line parallel to the given lines and placed between the two given lines.

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The locus of a point that is spaced equally from two concentric circles is the circle concentric with the given circles and is located midway between them.

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The locus of a point that is spaced equally from the sides of a given angle is the bisector of the angle.

### Locus Examples in Two Dimensional Geometry

Some of the locus examples in two-dimensional geometry are given below.

### Perpendicular Bisector

The set of points that bisect the line formed by joining two points and are at equal distance from the two points is known as perpendicular bisector.

### Angle Bisector

The set of points that bisect an angle and are at equal distance from two intersecting lines, which form the angle is known as the angle bisector.

### Ellipse

The set of points that satisfies the condition where the sum of the distance of two foci is constant defines an ellipse.

### Parabola

The set of points that are at equal distances from a fixed point and a line, is known as a parabola. The fixed point is the focus and the line is the directrix of the parabola.

### Hyperbola

There are two foci points in hyperbola, that are equidistant from the semi-major axis. The set of points that satisfies the condition where the absolute value of the difference between the distance of two given foci is constant, defines a hyperbola.

### Benefits of Selina Concise Mathematics Solutions by Vedantu

The exercises of the chapters are solved by the expert tutors at Vedantu to help students with their exam preparation and to secure good marks in the examination.

Solutions of each chapter are available in PDF format and can be downloaded free of cost to access offline.

Sums are solved in a stepwise method for a better understanding.

Apart from clearing doubts, these solutions also provide a comprehensive study of all the topics covered in this chapter.

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