NCERT Solutions for 11th Class Maths: Chapter 11-Conic Sections

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

NCERT Solutions for 11th Class Maths: Chapter 11-Conic Sections

NCERT 11th Maths Chapter 11, class 11 Maths Chapter 11 solutions

Exercise 11.1

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Question 11:
Find the equation of the circle passing through the points (2, 3) and (-1, 1) and whose centre is on the line x – 3y – 11 = 0.

Solution:

The equation of the circle is,
(x – h)2 + (y – k)2 = r2 ….(i)
Since the circle passes through point (2, 3)
∴ (2 – h)2 + (3 – k)2 = r2
⇒ 4 + h2 – 4h + 9 + k2 – 6k = r2
⇒ h2+ k2 – 4h – 6k + 13 = r2 ….(ii)
Also, the circle passes through point (-1, 1)
∴ (-1 – h)2 + (1 – k)2 = r2
⇒ 1 + h2 + 2h + 1 + k2 – 2k = r2
⇒ h2 + k2 + 2h – 2k + 2 = r2 ….(iii)
From (ii) and (iii), we have
h2 + k2 – 4h – 6k + 13 = h2 + k2 + 2h – 2k + 2
⇒ -6h – 4k = -11 ⇒ 6h + 4k = 11 …(iv)
Since the centre (h, k) of the circle lies on the line x – 3y-11 = 0.
∴ h – 3k – 11 = 0 ⇒ h -3k = 11 …(v)
Solving (iv) and (v), we get
h = 72 and k = −52
Putting these values of h and k in (ii), we get
(72)2+(−52)2−4×72−6×−52+13=r2
⇒ 494+254−14+15+13 ⇒ r2=652
Thus required equation of circle is
⇒ (x−72)2+(y+52)2=652
⇒ x2+494−7x+y2+254+5y=652
⇒ 4×2 + 49 – 28x + 4y2 + 25 + 20y = 130
⇒ 4×2 + 4y2 – 28x + 20y – 56 = 0
⇒ 4(x2 + y2 – 7x + 5y -14) = 0
⇒ x2 + y2 – 7x + 5y -14 = 0.

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Exercise 11.2

NCERT 11th Maths Chapter 11

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Exercise 11.3

NCERT 11th Maths Chapter 11

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Exercise 11.4

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Question 8.
Vertices (0, ±5), foci (0, ±8)

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Vertices are (0, ±5) which lie on x-axis. So the equation of hyperbola in standard form

 Question 9.
Vertices (0, ±3), foci (0, ±5)
Solution:
Vertices are (0, ±3) which lie on x-axis. So the equation of hyperbola in standard form

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NCERT 11th Maths Chapter 11, class 11 Maths Chapter 11 solutions

NCERT Solutions for 11th Class Maths: Chapter 11: Download PDF

NCERT Solutions for 11th Class Maths: Chapter 11-Conic Sections

Download PDF: NCERT Solutions for 11th Class Maths: Chapter 11-Conic Sections PDF

Chapterwise NCERT Solutions for Class 11 Maths :

• Chapter 1-Sets
• Chapter 2-Relations and Functions
• Chapter 3-Trigonometric Functions
• Chapter 4-Principle of Mathematical Induction
• Chapter 5-Complex Numbers and Quadratic Equations
• Chapter 6-Linear Inequalities
• Chapter 7-Permutation and Combinations
• Chapter 8-Binomial Theorem
• Chapter 9-Sequences and Series
• Chapter 10-Straight Lines
• Chapter 11-Conic Sections
• Chapter 12-Introduction to three Dimensional Geometry
• Chapter 13-Limits and Derivatives
• Chapter 14-Mathematical Reasoning
• Chapter 15-Statistics
• Chapter 16-Probability

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