NCERT solutions of class 11 maths exercise 11.3 chapter 11-Conic Section - Future Study Point

NCERT solutions of class 11 maths exercise 11.3 chapter 11-Conic Section

ncert solutions of ex.11.3 class 11 maths

NCERT solutions of class 11 maths exercise 11.3 chapter 11-Conic Section

Here all NCERT Solutions of Class 11 Maths Exercise 11.3 Chapter 11 Are Solved For Helping The Students of Class 11 In Clearing The Concept Of Chapter 11 Conic Section Completely So That They Could Attempt All The Questions Of The Chapter 11 Conic Section Mentioned In The Maths Question Paper Of CBSE Board Class 11.

Download pdf of NCERT solutions class 11 chapter 11-Conic Section

pdf-NCERT solutions class 11 chapter 11-Conic Section

ncert solutions of ex.11.3 class 11 maths

 

NCERT solutions of class 11 maths exercise 11.3 chapter 11-Conic Section

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

In each of the exercises 1 to 9,find the coordinates of the foci, the vertices, the length of major axis, the minor axis,the eccentricity and length of the latus rectum of the ellipse.

Ans. The given equation of the ellipse is

The equation of ellipse shows that major axis of the ellipse is along x-axis

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 36 ⇒ a = ±6 and b² = 16⇒b =±4

The coordinates of the foci are (±c,0)

c = √(a²-b²) = √(6² -4²) =√(36 -16) =√20

Therefore the coordinates of the foci are (±√20,0)

The vertices of the ellipse are (±a,0) = (±6,0)

The length of major axis is = 2a = 2× 6 = 12

The  length of minor axis = 2b = 2×4 = 8

The eccentricity of ellipse is = e =c/a = √20/6

Length of the latus rectum of the ellipse = 2b²/a =2×4²/6=16/3

 

Ans. The given equation of the ellipse is

The equation of ellipse shows that major axis of the ellipse is along y-axis(25>4)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

b² = 4 ⇒ b = ±2 and a² = 25⇒a =±5

The coordinates of the foci are (±c,0)

c = √(a²-b²) = √(5² -2²) =√(25 -4) =√21

Therefore the coordinates of the foci are (0,±√21)

The vertices of the ellipse are (0,±a) = (0,±5)

The length of major axis is = 2a = 2× 5 = 10

The  length of minor axis = 2b = 2×2 = 4

The eccentricity of ellipse is = e =c/a = √21/5

Length of the latus rectum of the ellipse = 2b²/a =2×2²/5=8/5

Ans. The given equation of the ellipse is

The equation of ellipse shows that major axis of the ellipse is along x-axis(16>9)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 16 ⇒ a = ±4  and b² = 9⇒b=±3

The coordinates of the foci are (±c,0)

c = √(a²-b²) = √(4² -3²) =√(16 -9) =√7

Therefore the coordinates of the foci are (±√7,0)

The vertices of the ellipse are (±a,0) = (±4,0)

The length of major axis is = 2a = 2× 4 = 8

The  length of minor axis = 2b = 2×3 = 6

The eccentricity of ellipse is = e =c/a = √7/4

Length of the latus rectum of the ellipse = 2b²/a =2×3²/4=9/2

Ans. The given equation of the ellipse is

The equation of ellipse shows that major axis of the ellipse is along y-axis(100>25)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 100⇒ a = ±10 and b² = 25⇒b=±5

The coordinates of the foci are (0,±c)

c = √(a²-b²) = √(10² -5²) =√(100 -25) =√75= 5√3

Therefore the coordinates of the foci are (0,±5√3)

The vertices of the ellipse are (0,±a) = (0,±10)

The length of major axis is = 2a = 2× 10= 20

The  length of minor axis = 2b = 2×5 = 10

The eccentricity of ellipse is = e =c/a = 5√3/10 =√3/2

Length of the latus rectum of the ellipse = 2b²/a =2×(5)²/10=5

NCERT solutions of class 11 maths exercise 11.3 chapter 11-Conic Section

Ans. The given equation of the ellipse is

The equation of ellipse shows that major axis of the ellipse is along y-axis(49>36)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 49⇒ a = ±7 and b² = 36⇒b=±6

The coordinates of the foci are (±c,0)

c = √(a²-b²) = √(7² -6²) =√(49-36) =√13

Therefore the coordinates of the foci are (±√13,0)

The vertices of the ellipse are (±a,0) = (±7,0)

The length of major axis is = 2a = 2× 7= 14

The  length of minor axis = 2b = 2×6= 12

The eccentricity of ellipse is = e =c/a = √13/7 =√13/7

Length of the latus rectum of the ellipse = 2b²/a =2×(6)²/7=72/7

Ans. The given equation of the ellipse is

The equation of ellipse shows that major axis of the ellipse is along y-axis (400>100)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 400⇒ a = ±20 and b² = 100⇒b=±10

The coordinates of the foci are (0,±c)

c = √(a²-b²) = √(400 -100) =√300 = 10√3

Therefore the coordinates of the foci are (0,±10√3)

The vertices of the ellipse are (0,±a) = (0,±20)

The length of major axis is = 2a = 2×20 = 40

The  length of minor axis = 2b = 2×10= 20

The eccentricity of ellipse is = e =c/a = 10√3/20  =√3/2

Length of the latus rectum of the ellipse = 2b²/a =2×(10)²/20=10

Ans. The given equation of the ellipse is

Rearranging the equation as follows

The equation of ellipse shows that major axis of the ellipse is along y-axis (36>4)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 36⇒ a = ±6 and b² = 4⇒b=±2

The coordinates of the foci are (0,±c)

c = √(a²-b²) = √(6² -2²) =√(36-4) =√32= 4√2

Therefore the coordinates of the foci are (0,±4√2)

The vertices of the ellipse are (0,±a) = (0,±6)

The length of major axis is = 2a = 2× 6= 12

The  length of minor axis = 2b = 2×2= 4

The eccentricity of ellipse is = e =c/a = 4√2/6 =2√2/3

Length of the latus rectum of the ellipse = 2b²/a =2×(2)²/6=4/3

Ans. The given equation of the ellipse is

Rearranging the equation as follows

The equation of ellipse shows that major axis of the ellipse is along y-axis (16>1)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 16⇒ a = ±4 and b² = 1⇒b=±1

The coordinates of the foci are (0,±c)

c = √(a²-b²) = √(4² -1²) =√(16-1) =√15

Therefore the coordinates of the foci are (0,±√15)

The vertices of the ellipse are (0,±a) = (0,±4)

The length of major axis is = 2a = 2× 4= 8

The  length of minor axis = 2b = 2×1= 2

The eccentricity of ellipse is = e =c/a = √15/4

Length of the latus rectum of the ellipse = 2b²/a =2×(1)²/4=1/2

Ans. The given equation of the ellipse is

Rearranging the equation as follows

The equation of ellipse shows that major axis of the ellipse is along y-axis (9>4)

The standard equation of ellipse is

On Comparing the given equation with the standard  equation,we get

a² = 9⇒ a = ±3 and b² = 4⇒b=±2

The coordinates of the foci are (±c,0)

c = √(a²-b²) = √(3² -2²) =√(9-4) =√5

Therefore the coordinates of the foci are (±√5,0)

The vertices of the ellipse are (±a,0) = (±3,0)

The length of major axis is = 2a = 2× 3= 6

The  length of minor axis = 2b = 2×2= 4

The eccentricity of ellipse is = e =c/a = √5/3

Length of the latus rectum of the ellipse = 2b²/a =2×(2)²/3=8/3

In each of the exercises 10 to 20,find the equations for the ellipse that satisfies the given conditions.

NCERT solutions of class 11 maths exercise 11.3 chapter 11-Conic Section

Ans. We are given the vertices (±a,0) = (±5,0), foci (±c,0) = (±4,0)

So,a = 5, c = 4

Since c² = a² – b² ⇒b =±√(a² -c²) =±√(5² – 4²) = ±√(25 -16) =±√9=±3

The equation of equation of ellipse is

Putting the value of a = 5 and b =3 in the equation

Q11. Vertices (0, ±13), foci (0, ± 5)

Ans. We are given the vertices (0,±a) = (0,±13), foci (0, ±c) = (0,±5)

So,a = 13, c = 5

Since c² = a² – b² ⇒b =±√(a² -c²) =±√(13² – 5²) = ±√(169 -25) =±√144=±12

The equation of equation of ellipse is

Putting the value of a = 13 and b =12 in the equation

Q12. Vertices (±6,0), foci ( ± 4,0)

Ans. We are given the vertices (±a,0) = (±6,0), foci ( ±c,0) = (±4,0)

So,a = 6, c = 4

Since c² = a² – b² ⇒b =±√(a² -c²) =±√(6² – 4²) = ±√(36 -16) =±√20=±2√5

The equation  of ellipse is

Putting the value of a = 6 and b =2√5  in the equation

Q13. Ends of the major axis (±3,0), ends of the minor axis (0, ± 2)

Ans. We are given the vertices i.e ends of the major axis (±a,0) = (±3,0), ends of the minor axis i.e (0,b) = (0, ± 2)

So,a = 3, b= 2

The equation of equation of ellipse is

Q14. Ends of the major axis (0,±√5), ends of the minor axis (± 1,0)

Ans. We are given the vertices i.e ends of the major axis (0, ±a) = (0,±√5), ends of the minor axis i.e (±b, 0) = (± 1,0)

So,a = √5, b= 1

The equation  of  the ellipse is

Q15. Length of major axis 26, foci (±5, 0)

Ans.We are given length of major axis 26, foci (±5, 0)

Length of major axis is 26 and foci (±5, 0)

Length of major axis, 2a = 26 ⇒ a = 13

Foci, (±c,0) = (±5, 0)⇒ c = 5

It is known that a2 = b+ c2.⇒b =±√(a²-c²) = ±√(13² – 5²)= ±√(169 – 25)=±√144=±12⇒b =12

The equation of the ellipse is

Putting the value of a =13, b = 12

NCERT solutions of class 11 maths exercise 11.3 chapter 11-Conic Section

16. Length of minor axis 16, foci (0, ±6).

Ans.We are given length of minor axis 16, foci (0,±6)

Length of minor axis, 2b = 16 ⇒ b = 8

Foci, (0, ±c) = (0, ±6)⇒ c = 6

It is known that a2 = b+ c2.⇒a =±√(b²+c²) = ±√(8² + 6²)= ±√(64 + 36)=±√100=±10⇒a =10

The equation of the ellipse is

Putting the value a =10,b =8

∴ The equation of the ellipse

Q17.Foci (±3, 0), a = 4

Ans. We are given that

Foci (±3, 0) and a = 4

Foci, ( ±c,0) = ( ±3,0)⇒ c = 3

It is known that a2 = b+ c2.⇒b =±√(a²-c²) = ±√(4² – 3²)= ±√(16- 9)=±√7=±√7⇒a =√7

The equation of ellipse is

Putting b = √7 and a = 4

Q18. b = 3, c = 4, centre at the origin; foci on the x axis.

Ans. We are given that

b = 3, c = 4, centre is(0,0) and foci on the x axis =(±c,0) = (±3,0)

It is known that a² = b² + c² ⇒ a =±√(b² +c²) = ±√(3² +4²) =±√25=±5

The equation of the ellipse is

Putting the value of a =5 and b =3

Q19. Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Ans. We are given centre of ellipse at (0,0) and it is passing through (3, 2) and (1, 6)

Major axis is on y-axis,so the eqation is

Putting the value of (x,y)= (3, 2) and (x,y) =(1, 6) in the equation,we get the equation (i) and equation (ii)

Solving (i) and (ii) equations

b² = 10 and a²= 40.

Substituting the value of b² = 10 and a²= 40 in the equation,we get the required equation

20. Major axis on the x-axis and passes through the points (4,3) and (6,2).

Ans. We are given that the ellipse is passing through (4, 3) and ( 6,2)

Major axis is on x-axis,so the eqation is

Putting the value of (x,y)= (4, 3) and (x,y) =(6, 2) in the equation,we get the equation (i) and equation (ii)

Solving (i) and (ii) equations

b² = 13 and a²= 52.

Substituting the value of b² = 13 and a²= 52 in the equation,we get the required equation

You can compensate us by donating any amount of money for our survival

Our Paytm NO 9891436286

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution

 

 

 

 

Scroll to Top