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S.L. Loney Equations Representing Two or More Straight Lines Solutions (Chapter 6)

SL Loney Elements of Coordinate Geometry Solutions Chapter 6 deals with equations representing two or more straight lines. The solutions for this chapter of SL Loney Solutions for Chapter 6 are prepared by the expert maths teachers at Instasolv with an aim to provide a fundamental aspect of mathematics to you. The solutions are a major reference guide to help you score well in the CBSE exams as well as the competitive exams like JEE Mains, JEE Advanced, and NEET.

Some of the main topics of this SL Loney Equations Representing Two or More Straight Lines Solutions are axes of coordinates, conditions of perpendicularity, general equation of the second degree, curve locus, discriminant of the general equation, straight line through the origin, and homogeneous expression. Practising the questions based on these topics will help you clear your concepts on the Equations that represent two or more straight lines.

Chapter 6 of SL Loney Solutions contains 3 main exercises with a total of 70 questions. Solving these exercise wise problems daily will help you improve your problem-solving skills, which are essential to achieve a better academic score. Following the solutions provided by Instasolv will help you in a better understanding of the chapter. Also, you can access these solutions from the comfort of your home at any time for free.

Important Topics for SL Loney Elements of Coordinate Geometry Solutions Chapter 6: Equations Representing Two or More Straight Lines

Equation Representing Straight Line 

The Equation representing the straight line is y = mx + c, where m is the gradient, and y = c is that value where the line cuts the y-axis. The intercept on the y-axis is referred to by the name c. The equation of a line with intercept c on the y-axis and gradient m is y = mx + c.

Axes of Coordinates

Coordinate axes are defined as when two unlimited straight numbered lines are perpendicular to one another on a surface such that their zero (0), zero (0) corresponds to one another to provide a point O (0,0) on the surface, then the whole plane is divided into four equivalent parts by the system, which is referred to as quadrants. The two straight lines are known as coordinate axes which are usually known as x-axis and y-axis.

Conditions of Perpendicularity

If two lines which are non-vertical and are within a similar surface having a similar slope, then these lines are known as parallel. These two parallel lines never intersect with each other.

If two lines which are non-vertical and are within a similar plane intersecting at a right angle then these lines are known as perpendicular. Horizontal and vertical lines are perpendicular to the axes of the coordinate plane. 

General Equation of the Second Degree

The general equation of the second degree in two variables which is a conic or limiting form of a conic

Ax2 + 2Bxy + Cy2 + 2Dx + 2Ey + F = 0

Any equation of the second degree in x and y comprising a term in xy are often transformed by a suitably chosen rotation into an equation containing no term in xy.

The rotation angle that will eliminate the term xy which is given by,

cot 2Ɵ = A – C/ 2B

Where the equations of the rotation transformation are

X = x’ cos Ɵ  – y’ sin Ɵ 

Y = x’ sin Ɵ  + y’ cos Ɵ

Curve Locus

A set of points where each and every point fulfils a specified condition is called a locus. Therefore, the locus is typically a curve. A locus can be a line, a parabola, a circle, a hyperbola, etc.

The Discriminant of the General Equation

The discriminant refers to that part beneath the square root within the quadratic formula, b²-4ac. The equation has existent solutions if it’s more than 0 (>0). There is not a solution if it is less than 0 (<0). There is only one solution if it is equivalent to 0(= 0).

Straight Lines through the Origin

The line that shows the possible values of x and y that satisfies the equation. The equation that signifies a straight line within the gradient ‘m’ passing through the origin is y = mx. The line passing through the origin, it always permits through the coordinates (0,0). 

Homogeneous Expression

If the sum of the power of the variables in each term is equivalent to n, then it is said to be a homogeneous expression of degree n which is also considered an expression in two or more than two variables.

Exercise-wise Discussion for SL Loney Elements of Coordinate Geometry Solutions Chapter 6: Equations Representing Two or More Straight Lines

There are 3 main exercises of this SL Loney Coordinate Geometry Equations Representing Two or More Straight Lines Solutions. The description of these exercises are listed below:

Exercise 1 – Short Answer Type Questions

This is the first exercise of the chapter where you will find 12 questions based on the main topics of the chapter including axes of coordinates, conditions of perpendicularity, and concepts of two straight lines. It is an important exercise from a competitive exam point of view. So, practice well with the help of the solutions provided by the experts of Instasolv.

Exercise 2 – Long Answer Questions

Exercise 2 of SL Loney Elements of Coordinate Geometry Solutions contains 17 questions based on the general equation of two straight lines and the general equation of the second degree. Practice these questions well to have a better understanding of the chapter.

Exercise 3 – High Order Thinking Questions

This exercise set of SL Loney Solutions for Chapter 6 contains a total of 41 questions. These questions are based on the important concepts of the chapter including straight lines through the origin. Practising the questions of this exercise will help you improve your analytical skills.

Why Use SL Loney Elements of Coordinate Geometry Solutions Chapter 6: Equations Representing Two or More Straight Lines by Instasolv?

  • The SL Loney Solutions for Chapter 6 ‘Equations Representing Two or More Straight Lines’ helps you in scoring good marks in the competitive exams like IIT JEE and NEET. 
  • All the solutions are based on the latest syllabus released by NCERT and majorly cover all the topics of the chapters in a well-structured format.
  • The SL Loney Elements of Coordinate Geometry Solutions are developed by qualified experts who are well-versed with the different techniques of teaching maths concepts.
  • Covering all the important topics of the chapters in systemic order is one of the major benefits this SL Loney Elements of Coordinate Geometry Solutions Chapter 6 provides to you.

Follow the NCERT Exemplar solutions provided by Instasolv now to excel in your exams!