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S.L. Loney The Straight-Line Polar Equation Oblique Co-Ordinates Solutions (Chapter 5)

SL Loney Elements of Coordinate Geometry Solutions Chapter 5 deals with the few basic concepts of the general equation to a straight line in polar coordinates. Referring to these solutions, you will learn about oblique coordinates. Other main topics of the chapter of SL Loney Solutions for The Straight Line Polar Equation Oblique Co-Ordinates include Cartesian Coordinates, straight line, the inclination of line, polar equation, the intersection of lines, and straight-line passing through the fixed points.

SL Loney The Straight Line Polar Equation Oblique Co-ordinates Solutions consists of 3 main exercises and 68 questions. The main aim to provide the solutions of this SL Loney Elements of Coordinate Geometry is to make you understand every concept of coordinate geometry clearly. All the solutions are prepared by the expert maths teachers at Instasolv. These solutions explain the steps with accuracy, without missing out on necessary parts of solving a question.

These SL Loney Chapter 5 Solutions, prepared by experts at Instasolv, are a comprehensive study material for you to prepare for the competitive exams like IIT JEE and NEET. These have been arranged for years as a complete source of material to you, to develop your analytical skills. Also, these solutions are easily accessible online. You can follow them anytime and anywhere.

Important Topics for SL Loney Elements of Coordinate Geometry Solutions Chapter 5: The Straight-Line Polar Equation Oblique Co-ordinates

Coordinate System

The two-dimensional number line is called a coordinate system, for instance, two perpendicular number lines or axes. The horizontal axis is named the x-axis and therefore the vertical axis is named the y-axis. The origin is defined as the centre of the coordinate system where the lines intersect. (0,0) is referred to as the coordinates of the origin.

Cartesian Coordinates

The two or three straight-line axes that outline the positions of points in 2D or 3D are known as the Cartesian coordinates also called rectangular coordinates. Each and every scale is graduated in increments of uniform size (i.e. all scales are linear).

Straight Line

A line is the set of all points between and increasing beyond two points. A line may be a primitive object that doesn’t have formal properties of length, its single dimension.

Inclination of Line 

The inclination of a non-horizontal line refers to the positive angle θ where that angel θ is less than 180 degrees and measured counterclockwise from the x-axis to the line. When the slope of this inclination line is positive, the angle of inclination is an acute angle. When the slope is negative, the angle of inclination is an obtuse angle.

Oblique Coordinates 

The above figure shows an oblique coordinate system. In such systems, the x-coordinate of a point is found by measuring the distance from the point to the y-axis parallel to the x-axis. Similarly, the y-coordinate of a point is found by measuring the distance from the point to the x-axis parallel to the y-axis. 

Polar Coordinates

Polar coordinates are referred to as the positions of points in 2D, consistent with the displacement from a central origin and therefore the angular displacement from a reference axis emanating from the origin. In some polar graphs, the radial axis is logarithmic but typically it is linear. The angles are often laid out in degrees or radian s and maybe measured counterclockwise or clockwise from the reference axis.

By the addition of an elevation axis that passes through the origin and perpendicular to the polar plane are the polar coordinates which get extended into 3D to become cylindrical coordinates. In some illustrations the elevation axis is logarithmic but typically it is linear.

Intersection of Lines

When two or more lines cross each other on a surface, then these lines are called intersecting lines. These lines share a mutual point, which exists on all the intersecting lines, and is referred to as the point of intersection.

Straight Line Passing through the Fixed Point

A straight line that passes through a stable point (h, k).The locus of the foot of the perpendicular on it drawn from the origin.

Exercise-wise Discussion for SL Loney Elements of Coordinate Geometry Solutions Chapter 5: The Straight-Line Polar Equation Oblique Co-ordinates

SL Loney Chapter 5 Solutions for Elements of Coordinate Geometry consists of solved examples as well as the exercises for practice. There are around 3 exercises that consist of a total of 68 questions. The description of these exercises are listed below:

Exercise 1 – Short Answer Type Questions

In this exercise of Chapter 5 ‘The Straight-Line Polar Equation Oblique Co-ordinates’ there are a total of 14 questions that are based on the basic concepts of the straight line.

Exercise 2 – Long Answer Type Questions

This exercise set of SL Loney Coordinate Geometry contains a total of 26 questions. These questions are based on the concepts of the straight line passing through fixed points. Practising these questions will make your concepts stronger.

Exercise 3 – High Order Thinking Questions

This is the last exercise of the SL Loney The Straight-Line Polar Equation Oblique Co-ordinates Solutions. It consists of a total of 28 questions which are based on the important topics like Cartesian Coordinates, straight line, the inclination of line, polar equation, the intersection of lines, and straight-line passing through the fixed points.

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