Conic Sections NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.1 11.2 11.3 11.4 Miscellaneous Free pdf Notes Study Material download-Anand Classes
NCERT solutions for Class 11 maths Chapter 11 Conic Sections sheds light on the types of curves commonly known as ellipses, parabolas, circles, and hyperbolas. These curves are known as conic sections or conics, which are obtained when a plane intersects with a double-napped right circular cone. Such curves are important in a wide range of applications, such as in the reflectors of flashlights, the study of planetary motion, antenna and telescope design. These NCERT solutions Class 11 maths Chapter 11 aim at providing information about the different types of curves as mentioned above with relevant practical examples.
Various kinds of conic sections are obtained depending on where the intersecting plane with respect to the cone is and what angle it makes with the vertical axis of the cone. This intersection can be at the vertex of the cone or on any other part of the nappe, above or below the vertex. These curves are critical tools for designing applications to explore space as well as study the behavior of atomic particles.
Download the pdf of NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections
Download the NCERT Book for Class 11 Maths Chapter 11 – Conic Sections
Number of questions in each exercise of NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections
The knowledge of various kinds of curves will help the students not only in mathematics but also in the understanding of other subjects like physics; hence it is advisable for the students to follow up on the basic facts and formulas as closely as possible. The pdf for the different exercises in the NCERT Solutions Class 11 Maths are given below :
- NCERT Solutions Class 11 Maths Chapter 11 Ex 11.1
- NCERT Solutions Class 11 Maths Chapter 11 Ex 11.2
- NCERT Solutions Class 11 Maths Chapter 11 Ex 11.3
- NCERT Solutions Class 11 Maths Chapter 11 Ex 11.4
- NCERT Solutions Class 11 Maths Chapter 11 Miscellaneous Ex
This chapter aims at exploring the various conic sections and explaining them with the help of well-illustrated diagrams. In-depth knowledge of the different curves has been provided in a lucid manner throughout, which the students must make use of by reading it carefully. This chapter consists of a number of formulas applied to different kinds of questions hence, students must make it a point to periodically revise them. An exercise-wise detailed analysis of NCERT Solutions Class 11 Maths Chapter 11 Conic Sections is given below :
- Class 11 Maths Chapter 11 Ex 11.1 – 15 Questions
- Class 11 Maths Chapter 11 Ex 11.2 – 12 Questions
- Class 11 Maths Chapter 11 Ex 11.3 – 20 Questions
- Class 11 Maths Chapter 11 Ex 11.4 – 15 Questions
- Class 11 Maths Chapter 11 Miscellaneous Ex 11.4 – 8 Questions
Important Topics and Subtopics of NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections
Topics Covered: The Class 11 maths NCERT solutions Chapter 11 covers the topics like circle, ellipse, parabola, hyperbola, degenerated conic sections, standard equations of such curves, the relationship between semi-major axis, semi-minor axis, and the distance of the focus from the center of the ellipse, as well as special cases of the ellipse. Further topics like eccentricity, and latus rectum are also explained.
Total Questions: Class 11 maths Chapter 11 Conic Sections consists of a total 70 questions of which 55 are easy, 10 are moderate and the remaining are long answer type questions.
List of Formulas in NCERT Solutions Class 11 Maths Chapter 11 – Conic Sections
The different curves talked about in this chapter have their own unique standard equations, as well as many formulas to determine the different parameters. Students are advised to pay attention to the derivation of these formulas as well, which will benefit them in understanding the underlying concepts. It is highly recommended that students make well-organized formula charts which will give them a quick recap of these concepts whenever required. The key to solving this chapter successfully is by memorizing the formulas. Some important ones covered in NCERT solutions for Class 11 maths Chapter 11 are given below :
- Standard Equation of Circle : If C (h, k) is the center and r is the radius of a circle, while P(x, y) is any point on the circle, then (x – h) 2 + (y – k) 2 = r 2
- Standard Equation of Ellipse : x2/b2 + y2/a2 = 1 wherein the center of the ellipse is the origin and ‘b’ and ‘a’ are the X and Y intercepts respectively.
- Equation of hyperbola with foci on x-axis : x2/a2 – y2/b2 = 1 where center is at the origin and ‘a’ is the distance from center to vertex and ‘c’ is the distance from center to foci and b2 = c2 – a2
- A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.
- The equation of a circle with centre (h, k) and the radius r is (x – h)2 + (y – k)2 = r2.
- A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane.
- The equation of the parabola with focus at (a, 0) a > 0 and directrix x = – a is y2 = 4ax.
- Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose endpoints lie on the parabola.
- Length of the latus rectum of the parabola y2 = 4ax is 4a.
- An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is constant.
- The equation of an ellipse with foci on the x-axis.
- Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose endpoints lie on the ellipse.
- Length of the latus rectum of the ellipse.
- The eccentricity of an ellipse is the ratio between the distances from the centre of the ellipse to one of the foci and to one of the vertices of the ellipse.
- A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is constant.
- The equation of a hyperbola with foci on the x-axis.
- Latus rectum of a hyperbola is a line segment perpendicular to the transverse axis through any of the foci and whose endpoints lie on the hyperbola.
- Length of the latus rectum of the hyperbola.
- The eccentricity of a hyperbola is the ratio of the distances from the centre of the hyperbola to one of the foci and to one of the vertices of the hyperbola.
Studying the Conic Sections of Class 11 enables the students to get a strong knowledge of the concepts of Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerate case of a conic section. The students would also be able to understand the standard equations and simple properties of parabola, ellipse, hyperbola and circle.
Frequently Asked Questions (FAQs) on NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections
Why are Class 11 Maths NCERT Solutions Chapter 11 Important?
The NCERT aims at providing easy access to knowledge for everyone through simple language. Hence, NCERT Solutions Class 11 Maths Chapter 11 are well researched by eminent scholars to present information in a relatable manner to the students with the help of solved practical examples. Also, the CBSE board highly recommends NCERT books for reference, making them an important learning resource.
Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths Conic Sections?
Mathematics, as we know, always gets better with practice. Regular practice helps with the consistent revision of concepts through trial and error. With the ample number of solved examples and questions provided in the NCERT Solutions Class 11 Maths Conic Sections, it is a good idea that the students make it a habit to solve all of these. This will increase their problem-solving skills giving them enough confidence to deal with any sort of questions related to curves.
What are the Important Topics Covered in NCERT Solutions Class 11 Maths Chapter 11?
The NCERT Solutions Class 11 Maths Chapter 11 explains the formation of different kinds of curves like, circle, ellipse, parabola, and hyperbola. It also talks about the standard equation of all of these curves. Further, it introduces the terms related to these curves, like the latus rectum, and eccentricity. students need to first understand the terms related to these curves and then move on to learning the formulas so as to score the best possible marks.
How Many Questions are there in NCERT Solutions Class 11 Maths Chapter 11 Conic Sections?
There are in total 70 questions in the NCERT Solutions Class 11 Maths Chapter 11 Conic Sections which have 55 easy problems, 10 moderately easy while the remaining are a bit difficult. The students must make note of all the important formulas given throughout the book to ensure that they can progress through these sums smoothly.
Why Should I Practice Class 11 Maths NCERT Solutions Conic Sections Chapter 11?
The NCERT Solutions Class 11 Maths Conic Sections Chapter 10 will help students improve their problem-solving and mental math skills. These answers will provide them with enough practice on working with the equations of different types of curves, be it parabola, circle or ellipse. These topics form a major foundation of the topics taught in the higher classes, thus it is critical to building their fundamentals from this chapter. Hence, students must practice each and every question.
How CBSE Students can utilize NCERT Solutions Class 11 Maths Chapter 11 effectively?
The NCERT Solutions Class 11 Maths Chapter 11 has well-researched content on the different types of curves written by notable scholars in simple language. This makes it easy for the students to understand not only the logic behind these curves but also their practical implications. There are extensive solved examples and questions which the students must practice every day. Also, the important formulas and facts are offered in the chapter’s highlights section at the end, which students can refer to when in doubt. In this way, they can utilize this resource effectively.
How to score good marks in Chapter 11 of NCERT Solutions for Class 11 Maths?
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