Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections

Class 11: Maths Chapter 7 solutions. Complete Class 11 Maths Chapter 1 Notes.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections

Maharashtra Board 11th Maths Chapter 7, Class 11 Maths Chapter 7 solutions

Ex 7.1

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1

ii) Given equation of the parabola is y2 = -20x.
Comparing this equation with y2 = -4ax, we get
⇒ 4a = 20
⇒ a = 5
Co-ordinates of focus are S(-a, 0), i.e., S(-5, 0)
Equation of the directrix is x – a = 0
⇒ x – 5 = 0
Length of latus rectum = 4a = 4(5) = 20
Co-ordinates of end points of latus rectum are (-a, 2a) and (-a, -2a),
⇒ (-5, 10) and (-5, -10).

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1

∴ The required equation of the parabola is x2 = -4(5)y, i.e., x2 = -20y.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1

Question 4.
Find the equation of the parabola whose vertex is O(0, 0) and focus at (-7, 0).
Solution:

Focus of the parabola is S(-7, 0) and vertex is O(0, 0).
Since focus lies on X-axis, it is the axis of the parabola.
Focus S(-7, 0) lies on the left-hand side of the origin.
It is a left-handed parabola.
Required parabola is y = -4ax.
Focus is S(-a, 0).
a = 7
∴ The required equation of the parabola is y2 =-4(7)x, i.e., y2 = -28x.

Question 5.
Find the equation of the parabola with vertex at the origin, the axis along X-axis, and passing through the point
(i) (1, -6)
(ii) (2, 3)
Solution:

(i) Vertex of the parabola is at origin (0, 0) and its axis is along X-axis.
Equation of the parabola can be either y2 = 4ax or y2 = -4ax.
Since the parabola passes through (1, -6), it lies in the 4th quadrant.
Required parabola is y2 = 4ax.
Substituting x = 1 and y = -6 in y2 = 4ax, we get
⇒ (-6)2 = 4a(1)
⇒ 36 = 4a
⇒ a = 9
∴ The required equation of the parabola is y2 = 4(9)x, i.e., y2 = 36x.

(ii) Vertex of the parabola is at origin (0, 0) and its axis is along X-axis.
Equation of the parabola can be either y2 = 4ax or y2 = -4ax.
Since the parabola passes through (2, 3), it lies in 1st quadrant.
∴ Required parabola is y2 = 4ax.
Substituting x = 2 and y = 3 in y2 = 4ax, we get
⇒ (3)2 = 4a(2)
⇒ 9 = 8a

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1

⇒ a = 1
Focal distance of a point = x + a
Given, focal distance = 17
⇒ x + 1 = 17
⇒ x = 16
Substituting x = 16 in y2 = 4x, we get
⇒ y2 = 4(16)
⇒ y2 = 64
⇒ y = ±8
∴ The co-ordinates of the point on the parabola are (16, 8) or (16, -8).

Question 10.
Find the length of the latus rectum of the parabola y2 = 4ax passing through the point (2, -6).
Solution:

Given equation of the parabola is y2 = 4ax and it passes through point (2, -6).
Substituting x = 2 and y = -6 in y2 = 4ax, we get
⇒ (-6)2 = 4a(2)
⇒ 4a = 18
∴ Length of latus rectum = 4a = 18 units

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1

Question 12.
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus.
Solution:

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1

Let LOM be the parabolic reflector such that LM is the diameter and ON is its depth.
It is given that ON = 5 cm and LM = 20 cm.
LN = 10 cm
Taking O as the origin, ON along X-axis and a line through O ⊥ ON as Y-axis.
Let the equation of the reflector be y2 = 4ax ……(i)
The point L has the co-ordinates (5, 10) and lies on parabola given by (i).
Substituting x = 5 and y = 10 in (i), we get
⇒ 102 = 4a(5)
⇒ 100 = 20a
⇒ a = 5
Focus is at (a, 0), i.e., (5, 0)

Question 13.
Find co-ordinates of focus, vertex, and equation of directrix and the axis of the parabola y = x2 – 2x + 3.
Solution:

Given equation of the parabola is y = x2 – 2x + 3
⇒ y = x2 – 2x + 1 + 2
⇒ y – 2 = (x – 1)2
⇒ (x – 1)2 = y – 2
Comparing this equation with X2 = 4bY, we get
X = x – 1, Y = y – 2
⇒ 4b = 1

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.1

Ex 7.2

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2

Length of minor axis = 2b = 2√3
Lengths of the principal axes are 4 and 2√3.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2

Since a > b,
X-axis is the major axis and Y-axis is the minor axis.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.2

Ex 7.3

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3

⇒ b = 5 and a = 3
Length of transverse axis = 2b = 2(5) = 10
Length of conjugate axis = 2a = 2(3) = 6
Co-ordinates of vertices are B(0, b) and B’ (0, -b),
i.e., B(0, 5) and B’ (0, -5)
We know that

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3

Solution:
Let e be the eccentricity of a hyperbola

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3

Question 5.
Find the equation of the hyperbola referred to its principal axes:

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections Ex 7.3

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Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 7- Conic Sections

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Chapterwise Maharashtra Board Solutions Class 11 Arts & Science Maths (Part 1) :

FAQs

Where do I get the Maharashtra State Board Books PDF For free download?

You can download the Maharashtra State Board Books from the eBalbharti official website, i.e. cart.ebalbharati.in or from this article.

How to Download Maharashtra State Board Books?

Students can get the Maharashtra Books for primary, secondary, and senior secondary classes from here.  You can view or download the Maharashtra State Board Books from this page or from the official website for free of cost. Students can follow the detailed steps below to visit the official website and download the e-books for all subjects or a specific subject in different mediums.
Step 1: Visit the official website ebalbharati.in
Step 2: On the top of the screen, select “Download PDF textbooks” 
Step 3: From the “Classes” section, select your class.
Step 4: From “Medium”, select the medium suitable to you.
Step 5: All Maharashtra board books for your class will now be displayed on the right side. 
Step 6: Click on the “Download” option to download the PDF book.

Who developed the Maharashtra State board books?

As of now, the MSCERT and Balbharti are responsible for the syllabus and textbooks of Classes 1 to 8, while Classes 9 and 10 are under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE).

How many state boards are there in Maharashtra?

The Maharashtra State Board of Secondary & Higher Secondary Education, conducts the HSC and SSC Examinations in the state of Maharashtra through its nine Divisional Boards located at Pune, Mumbai, Aurangabad, Nasik, Kolhapur, Amravati, Latur, Nagpur and Ratnagiri.

About Maharashtra State Board (MSBSHSE)

The Maharashtra State Board of Secondary and Higher Secondary Education or MSBSHSE (Marathi: महाराष्ट्र राज्य माध्यमिक आणि उच्च माध्यमिक शिक्षण मंडळ), is an autonomous and statutory body established in 1965. The board was amended in the year 1977 under the provisions of the Maharashtra Act No. 41 of 1965.

The Maharashtra State Board of Secondary & Higher Secondary Education (MSBSHSE), Pune is an independent body of the Maharashtra Government. There are more than 1.4 million students that appear in the examination every year. The Maha State Board conducts the board examination twice a year. This board conducts the examination for SSC and HSC. 

The Maharashtra government established the Maharashtra State Bureau of Textbook Production and Curriculum Research, also commonly referred to as Ebalbharati, in 1967 to take up the responsibility of providing quality textbooks to students from all classes studying under the Maharashtra State Board. MSBHSE prepares and updates the curriculum to provide holistic development for students. It is designed to tackle the difficulty in understanding the concepts with simple language with simple illustrations. Every year around 10 lakh students are enrolled in schools that are affiliated with the Maharashtra State Board.

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