NCERT solutions of class 11 maths exercise 11.2 chapter 11-Conic sections - Future Study Point

NCERT solutions of class 11 maths exercise 11.2 chapter 11-Conic sections

NCERT solutions exercise 11.2 class 11 maths

NCERT solutions of class 11 maths exercise 11.2 -Conic sections

NCERT solutions exercise 11.2 class 11 maths

All the NCERT solutions of class 11 maths exercise 11.2 chapter 11-Conic sections are created here are the solutions of unsolved questions of the chapter 11-conic sections which is one of the important chapter.The concept of the chapter conic section of NCERT text book is utilised in the industry and science and technology as an example planetry motion,in designing telescope,antennas,reflector in flashlights and automobile headlights.Conic sections are actually the surfaces generated by the intersection of a plane on a double napped right circular cone.

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

pdf-NCERT solutions class 11 chapter 11-Conic Section

All the NCERT solutions are explained by an expert of maths,each NCERT solutions are explained here by a step by step method,so every students can understand it properly,it will help all the students of class 11 studens in boosting their preparation of fortcomming CBSE board exams.

NCERT solutions of class 11 maths exercise 11.2 -Conic sections

Q1.Find the coordinates of the focus, axis of parabola, the equation of directrix and the length of the lactus rectum for y² = 12x

Click for online shopping

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

Ans. The given equation is y² = 12x

Here, coefficient of x is positive. Hence, the parabola opens toward the right.

On comparing the equation with y² = 4ax, we obtain

4a = 12

a = 12/4

a = 3

Coordinates of the focus = (a,0) = (3,0)

Since the given equation involves y², the axis of the parabola is the x-axis.

Equation of directrix, x = -a

Length of lactus rectum = 4a = 4 × 3 = 12

Q2.Find the coordinates of the focus, axis of parabola, the equation of directrix and the length of the lactus rectum for x² = 6y

Ans. The given equation is x² = 6y

Here, coefficient of y is positive. Hence, the parabola opens upwards.

On comparing the equation with x² = 4ay, we obtain

6y = 4ay

4a = 6

a = 6/4

a = 3/2

Coordinates of the focus = (0,a) = (0,3/2)

Since the given equation involves x², the axis of the parabola is the y-axis.

Equation of directrix, y = -a

Length of lactus rectum = 4a = 6

Q3.Find the coordinates of the focus, axis of parabola, the equation of directrix and the length of the lactus rectum for y² = -8x

Ans. The given equation is y² = -8x

Here, coefficient of x is negative. Hence, the parabola opens towards the left.

On comparing the equation with y² = -4ax, we obtain

-4a = -8

a = 8/4

a = 2

Coordinates of the focus = (-a,o) = (-2,0)

Since the given equation involves y², the axis of the parabola is the x-axis.

Equation of directrix, x = a

Length of lactus rectum = 4a = 8

Q4.Find the coordinates of the focus, axis of parabola, the equation of directrix and the length of the lactus rectum for x² = -16y

Ans. The given equation is x² = -16y

Here, coefficient of y is negative. Hence, the parabola opens downwards.

On comparing the equation with x² = -4ay, we obtain

-4a = -16

a = 16/4

a = 4

Coordinates of the focus = (o,-a) = (0,-4)

Since the given equation involves x², the axis of the parabola is the y-axis.

Equation of directrix, y = a

Length of lactus rectum = 4a = 16

Q5.Find the coordinates of the focus, axis of parabola, the equation of directrix and the length of the lactus rectum for y² = 10x

Ans. The given equation is y² = 10x

Here, coefficient of x is positive. Hence, the parabola opens towards the right.

On comparing the equation with y² = 4ax, we obtain

4a = 10

a = 10/4

a = 5/2

Coordinates of the focus = (a,o) = (5/2,0)

Since the given equation involves y², the axis of the parabola is the x-axis.

Equation of directrix, x = -a⇒ x = -5/2

Length of lactus rectum = 4a = 4×5/2 =10

NCERT solutions of class 11 maths exercise 11.2 -Conic sections

Q6.Find the coordinates of the focus ,axis of parabola ,the equation of directrix and length of latus rectum for x² = -9y.

Ans. The given equation of the parabola is x² = -9y

Comparing the given equation with the standard equation of parabola

x² = 4ay

4a = -9

a = -9/4

Coordinates of the focus = (a,0) =(-9/4, 0)

Since the given equation(x² =-9y) is symmetric about y-axis  so the axis of parabola is y-axis

The equation of directrix= x = -a⇒x = -(-9/4) ⇒x =9/4

And length of latus rectum =4a = 4×9/4 =9

In each of the section of the exercises 7 to 12, find the equation of the parabola that satisfies the given conditions.

Q7. Focus (6,0), directrix x = -6

Ans. Focus of the parabola is : (a,0) and directrix x = -a

We are given here focus : (6,0)=(a,0)⇒ a = 6

directrix is x =-6 indicates that the parabola is symmetric about x-axis and negative sign shows that it opens at left side of y-axis

So,the equation of parabola is y² = 4ax

Putting a = 6,we get

y² = 4×6x⇒ y² = 24x

y² = 24x

Q8.Focus (0,-3): direcrix, y = 3

Ans. Focus of the parabola is : (0,a) and directrix y= -a

We are given here focus : (0,a)=(0,-3)⇒ a = -3 and directrix y =3

directrix is y =3 indicates that the parabola is symmetric about y-axis and positive sign shows that it opens downwards of x -axis

So,the equation of parabola is x² = 4ay

Putting a = -3,we get

x² = 4×-3y⇒ x² = -12y

x² = -12y

Q9.Vertex (0,0): focus (3,0)

Ans. Focus of the parabola is : (a,0) and the coordinates of the vertex are (0,0)

We are given here focus : (a,0)=(3,0)⇒ a = 3 and directrix will be x= -a ⇒x = -3

directrix is x = -3 indicates that the parabola is symmetric about x-axis and negative sign shows that it opens right of y -axis

So,the equation of parabola is y² = 4ax

Putting a = 3,we get

y² = 4×3x⇒ y² = 12x

y² = 12x

Q10.Vertex (0,0) : focus (-2,0)

Ans. Focus of the parabola is : (a,0) and the coordinates of the vertex are (0,0)

We are given here focus : (a,0)=(-2,0)⇒ a = -2 and directrix will be x= -a ⇒x = -(-2) = 2⇒ x = 2

directrix is x = 2 indicates that the parabola is symmetric about x-axis and positive sign shows that it opens left of y -axis

Equation of parabola is y² = 4ax

Putting a = -2,we get

y² = 4×-2x⇒ y² = -8x

y² = -8x

Q11. Vertex (0,0) passing through (2,3) and axis is along x-axis.

Ans. Since axis of parabola is on x-axis therefore equation of parabola is

y² =4ax, it is given to us that parabola is passing through (2,3)

Putting x =2,y =3 in the equation of parabola

3² = 4×a×2⇒a =9/8

The focus of parabola is : (a,0)=(9/8,0)⇒ a = 9/8 and directrix will be x= -a ⇒x = -9/8

directrix is x = -9/8 indicates that the parabola is symmetric about x-axis and negative sign shows that it opens right of y -axis

So,the equation of parabola is

y² =4ax, putting a =9/8 in the equation

y² = 4×(9/8)x

2y² =9x

NCERT solutions of class 11 maths exercise 11.2 -Conic sections

Q12.Vertex (0,0) passing through (5,2) and symmetric with respect to y-axis.

Ans. Since axis of parabola is symmetric with respect to y-axis. therefore equation of parabola is

x² =4ay, it is given to us that parabola is passing through (5,2)

Putting x =5,y =2 in the equation of parabola

5² = 4×a×2 ⇒a =25/8

The focus of parabola is : (0,a)=(0,25/8)⇒ a = 25/8 and directrix will be y= -a⇒x = -25/8

directrix is x = -25/8 indicates that the parabola is symmetric about x-axis and negative sign shows that it opens right of y -axis

So,the equation of parabola is

x² =4ay, putting a =25/8 in the equation

x² = 4×(25/8)y

x² =(25/2)x ⇒2x² =25y

What are Surds and how to compare them?(useful for competitive exams)

Study notes of Maths and Science NCERT and CBSE from class 9 to 12

Solutions of Class 11 maths test unit-2 G.D Lancer Public School,New Delhi

Class 11 Maths solutions of important questions of chapter 1-Sets

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