NCERT Solutions For Class 11 Maths Chapter 11: Conic Sections

Content Curator

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections are provided in the article. Conic section is a curve formed by intersecting a plane with a cone. The curves that are formed are Circles, Ellipse, Parabola, and Hyperbola.

Download: NCERT Solutions for Class 11 Mathematics Chapter 11 pdf

Class 11 Maths NCERT Solutions Chapter 11 Conic Sectios

Class 11 Maths NCERT Solutions Chapter 11 Conic Sections are provided below:

Also read: Concept Notes on Conic Sections

Important Topics: Class 11 Maths NCERT Solutions Chapter 11 Conic Sections

Important Topics Class 11 Maths NCERT Solutions Chapter 11 Conic Sections are elaborated below:

Sections of a Cone

There are three sections of a cone or conic sections: Parabola, Hyperbola, and Ellipse (Circle is a special kind of Ellipse).

Circle

Circle is the simplest conic section. As a conic section, circle is intersection of a plane perpendicular to the cone's axis.

Please Note:

Value of eccentricity(e) for a circle is e = 0.

Circle has no directrix.

General form of the equation of a circle with center at (h, k), and radius r: (x−h)² + (y−k)² = r²

Parabola

When intersecting plane is at an angle to the surface of the cone, thwe obtained conic section is called the parabola. It is a U-shaped conic section.

The value of eccentricity(e) for parabola is e = 1

Ellipse

Ellipse is a conic section that is formed when plane intersects with cone at an angle. Ellipse has 2 foci, a major axis, as well as a minor axis.

Please Note:

Value of eccentricity(e) for ellipse is e < 1.
Ellipse has 2 directrices.
The conic section formula for an ellipse is: (x−h)²/a² + (y−k)²/b² = 1

Hyperbola

Hyperbola is formed when interesting plane is parallel to axis of the cone, and intersect with both nappes of the double cone.

General form of equation of hyperbola with (h, k) as the center is:

(x−h)²/a² - (y−k)²/b² = 1

NCERT Solutions For Class 11 Maths Chapter 11 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 11 Conic Sections under different exercises are as follows:

Also check:

Chapter Related Topics
Eccentricity of Ellipse	Latus rectum of Ellipse	Parabola Formula
Latus rectum of Hyperbola	Eccentricity	Locus

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

View Solution

2.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

View Solution

3.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

View Solution

4.
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

f is one-one onto
f is many-one onto
f is one-one but not onto
f is neither one-one nor onto

View Solution

5.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

View Solution

6.
Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).

View Solution

View All

Similar Mathematics Concepts

Conic Sections: Formula, Equations & Examples

Conic Sections: Parabola, Hyperbola, Ellipse, Circle

Parabola Formula: Vertex, Focus, Directrix

Conic Sections: Important Questions

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.3

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

CBSE CLASS XII Previous Year Papers

Mathematics

Mathematics Preparation Guides

Sequence and Series: Types, Formulas & Examples

Measures of Dispersion: Types, Absolute & Relative measure

Events and their Types in Probability

Angle between two lines: Derivation, Types, Formulae

Mathematics: Latus rectum of Ellipse- Definition, Equation, Examples and Sample Questions

Pascal’s Triangle: Construction, Notation, Pattern, Properties

Ellipse: Standard Equation, Derivation & Formula

Circle: Definition, Equation and Segments

Geometric Progression: Definition, Sum of N Terms, Formula

Conic Sections: Formula, Equations & Examples

Parabola: Graph, General Equation, Formulae, Latus Rectum, Focal, Normal , Tangent, Sample Questions

Horizontal and Vertical Lines: Formula, Examples & Equations

Conic Sections: Parabola, Hyperbola, Ellipse, Circle

Eccentricity of Ellipse Formula, Definition, Derivation & Examples

Complex Numbers and Quadratic Equations

Real Valued Functions: Types, Operations & Examples

Latus Rectum of Parabola: Formula, Length & Derivation

Venn Diagrams: Symbols, Formula, Set Operations & Examples

Types of Events in Probability

Types of Sets: What is Set, Examples & Symbols

Mathematics NCERT Solutions

Factorial Formula: Calculation, Values, Application

Multiplication Rule of Probability: Proof and Solved Examples

Logarithms: Rules, Properties and Formula

Mathematical Logic: Conjunction, Disjunction and Negation

Value of Log 1: Logarithmic Functions, Value of In 1, Logarithmic Values

Solving Inequalities

Tautology: Operators, Logic Symbols, and Truth Table

Quotient Rule: Definition, Formula, Applications and Sample Questions

Conjugate of a Complex Number: Definition, Properties and Equations

Difference between Ln and Log: Definitions and Properties

You can also check

NCERT Solutions For Class 11 Maths Chapter 11: Conic Sections

Class 11 Maths NCERT Solutions Chapter 11 Conic Sectios

Important Topics: Class 11 Maths NCERT Solutions Chapter 11 Conic Sections

NCERT Solutions For Class 11 Maths Chapter 11 Exercises:

CBSE CLASS XII Related Questions

1.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

2.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

3.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

4.
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

5.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

6.
Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

NCERT Solutions For Class 11 Maths Chapter 11: Conic Sections

Class 11 Maths NCERT Solutions Chapter 11 Conic Sectios

Important Topics: Class 11 Maths NCERT Solutions Chapter 11 Conic Sections

NCERT Solutions For Class 11 Maths Chapter 11 Exercises:

CBSE CLASS XII Related Questions

1. Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

2. If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that (i) \((A+B)'=A'+B' \)(ii) \((A-B)'=A'-B'\)

3. Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

4. Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

5. Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)n=anI+nan-1bA,where I is the identity matrix of order 2 and n∈N

6. Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

2.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

3.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

4.
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

5.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

6.
Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).