# Ex 9.3, 10 - Chapter 9 Class 12 Differential Equations

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

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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.