NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.2 Straight Lines - PDF Download

NCERT solution for class 11 maths chapter 9 exercise 9.2 Straight Lines provides information on various forms of the equation of a line. A straight line point can be defined in its entirety using the input values from coordinate geometry. This is one of the most powerful methods of determining the position of points on a line so that a line can be drawn through them. For a particular set of lines, you can determine whether the lines intersect each other, if they are parallel, what angle they intersect at, or at which point they intersect.

Class 11 maths chapter 9 exercise 9.2 NCERT solutions is composed of 19 questions from which some questions are short answer type and some are long answer type. The purpose of the questions is tofindout the various types of slope of a line. These include Point-Slope, Two-Point, Slope-Intercept, and Intercepts, all of which can be used to determine a line's slope under various constraints. Ex 9.2 class 11 maths solutions are prepared by the academic team of mathematics which give thorough comprehension of each topic mentioned above. To prepare for exams, Students can also download the free PDF solutions available on eSaral website. The solutions PDF can be downloaded from the given link below.

Topics Covered in Exercise 9.2 Class 11 Mathematics Questions

Ex 9.2 class 11 maths chapter 9 has some significant topics such as various forms of the equation of a line like horizontal and vertical lines, point-slope form, two-point form,  slope-intercept form and intercept-form. All of these topics are explained below for your reference. 

1. Various Forms of the Equation of a Line

In this section, we will discuss the equation for a line under various conditions.

• Horizontal and vertical lines

If a horizontal line L is at a distance a from the x axis then the ordinate of every point lying on the line is either a or – a. Therefore, the equation of the line L is either y = a or y = – a. Choice of sign will depend upon the position of the line according as the line is above or below the y-axis. 

Similarly, the equation of a vertical line at a distance b from the y-axis is either x = b or x = – b 

• Point-slope form

If P₀ (x₀ , y₀ ) is a fixed point on a non-vertical line L, whose slope is m. Let P (x, y) be an arbitrary point on L.

Then, by the definition, the slope of L is given by 

m = $\frac{y-y_0}{x-x_0}$

y- y0 = m(x-x0)

• Two-point form

Line L passes through two given points P₁ (x₁ , y₁ ) and P₂ (x₂ , y₂ ). Let P (x, y) be a general point on L

The three points P₁ , P₂ and P are collinear, therefore, we have slope of P₁ P = slope of P₁ P₂

Thus, equation of the line passing through the points (x₁ , y₁ )and (x₂ , y₂ ) is given by

$\mathrm{y}-\mathrm{y}_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

• Slope-intercept form

Let's say you have a line with a slope of m that cuts the Y-axis at a distance ‘a’ from the origin. The distance ‘a’ from the origin is called the y intercept of the line. (0, a) is the point where the line cuts the y axis.

Then, the line equation will be

y- a= m(x-0)

y=mx+a

Similarly, let's say we have a straight line with a slope of m that cuts the X- axis at a distance b from the origin will be at a point (b,0). The x-intercept of the line is the distance b.

The equation for the line will be:

y = m(x-b)

• Intercept - form

A line L makes x-intercept a and y-intercept b on the axes. Obviously L meets x-axis at the point (a, 0) and y-axis at the point (0, b)

By two-point form of the equation of the line

y-0 = $\frac{b-0}{0-a}$ (x-a) or  ay= -bx + ab

Thus, equation of the line making intercepts a and b on x-and y-axis, respectively, is

$\frac{x}{a}+\frac{y}{b}$=1

Tips for Solving Exercise 9.2 Class 11 Chapter 9 Straight Lines

To understand the concepts, terms and definitions of topics included in ex 9.2 chapter 9 class 11 maths, Our subject experts have provided tips and methods to solve ex 9.2 questions.

1. Students should comprehend the various forms of the equations of a line before solving the exercise questions.

2. You must be well-versed with every concept associated with the questions of ex 9.2.

3. Students should also solve the examples provided before the exercise for better understanding of concepts.

4. You must solve the questions provided in NCERT solutions by eSaral class 11 maths chapter 9 ex 9.2.
   

Importance of Solving Ex 9.2 Class 11 Maths Chapter 9 Straight Lines

Solving ex 9.2 class 11 maths ch 9 has a lot of benefits. Students can find here some of them which are provided by expert teachers of eSaral.

1. Exercise 9.2 class 11 maths is very important to understand the various forms of the equations of a line. By solving questions of ex 9.2, you can get the most of it.

2. You will be benefited the most if you solve NCERT solutions ex 9.2 class 11 maths questions again and again.

3. Solving questions in NCERT solutions class 11 maths chapter 9 ex 9.2 will reduce your doubts and maximize your accuracy of solving questions.

4. NCERT solutions are also available here in PDF format which will help you to cross check your answer that will boost your confidence.
   

Frequently Asked Questions 

Question 1. What are key topics covered in NCERT solutions class 11 maths chapter 9 ex 9.2?

Answer 1. The key topics covered in NCERT solutions class 11 maths chapter 9 ex 9.2 are various forms of the equation of a line like horizontal and vertical lines, point-slope form, two-point form, slope-intercept form and Intercept - form. You will find the detailed solutions of all the topics in PDF format provided by eSaral.  

Question 2. Where can I download the PDF of NCERT solutions for ex 9.2 class 11 maths chapter 9?

Answer 2. You can download the PDF of NCERT solutions for ex 9.2 class 11 maths chapter 9 from the official website of eSaral.