# Ex 9.3, 10

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 9.3, 10 Form the differential equation of the family of circle having a center on 𝑦−𝑎𝑥𝑖𝑠 and radius 3 units. General equation of circle is :- 𝑥−𝑎2+ 𝑦−𝑏2= 𝑟2 Given center is on y-axis & radius = 3 units ∴ Center = (0, b) Hence, our equation becomes 𝑥−02+ 𝑦−𝑏2= 32 𝑥2+ 𝑦−𝑏2=9 Differentiating Both Sides w.r.t. 𝑥 2𝑥+2 𝑦−𝑏 𝑑𝑦𝑑𝑥−0=0 2 𝑥+ 𝑦−𝑏 𝑑𝑦𝑑𝑥=0 𝑥+ 𝑦−𝑏 𝑑𝑦𝑑𝑥=0 𝑦−𝑏 𝑑𝑦𝑑𝑥=−𝑥 𝑦−𝑐= −𝑥 𝑑𝑦𝑑𝑥 Putting the value of 𝑦−𝑏 in equation (1) x2 + (y − c)2 = 9 𝑥2+ −𝑥 𝑑𝑦𝑑𝑥2=9 𝑥2+ 𝑥2 𝑑𝑦𝑑𝑥2=9 𝑥2 𝑑𝑦𝑑𝑥2+ 𝑥2 𝑑𝑦𝑑𝑥2=9 𝑥2 𝑑𝑦𝑑𝑥2+ 𝑥2=9 𝑑𝑦𝑑𝑥2 𝑥2 𝑦′2+ 𝑥2=9 𝑦′2 𝑥2 𝑦′2−9 𝑦′2+ 𝑥2=0 𝑦′2 𝑥2−9+ 𝑥2=0 ∴ 𝒙𝟐−𝟗 𝒚′𝟐+ 𝒙𝟐=𝟎

Chapter 9 Class 12 Differential Equations

Example 1
Important

Ex 9.1, 11 Important

Ex 9.1, 12 Important

Example 7 Important

Ex 9.3, 7 Important

Ex 9.3, 10 Important You are here

Example 13 Important

Ex 9.4, 14 Important

Example 17 Important

Example 18 Important

Ex 9.5, 8 Important

Ex 9.5, 15 Important

Example 22 Important

Ex 9.6, 7 Important

Ex 9.6, 13 Important

Ex 9.6, 14 Important

Example 25 Important

Example 27 Important

Example 28 Important

Misc 6 Important

Misc 11 Important

Misc 12 Important

Misc 13 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.