# Misc 5

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Misc 5 Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes . Drawing figure : Let C be the family of circles in first quadrant touching coordinate. Let radius be 𝑎 ∴ Center of circle = (−𝑎, 𝑎) Thus, Equation of a circle is 𝑥−𝑎2+ 𝑦−𝑎2= 𝑎2 𝑥2+ 𝑎2−2𝑎𝑥+ 𝑦2+ 𝑎2−2𝑎𝑥= 𝑎2 𝑥2+ 𝑦2−2𝑎𝑥−2𝑎𝑦+ 𝑎2=0 Since there is only one variable , we differentiate once Differentiating w.r.t. 𝑥 both Sides 𝑑 𝑥2 + 𝑦2 − 2𝑎𝑥 − 2𝑎𝑦+ 𝑎2𝑑𝑥= 𝑑𝑑𝑥 0 2𝑥+2𝑦 𝑑𝑦𝑑𝑥−2𝑎−2𝑎 𝑑𝑦𝑑𝑥+0=0 𝑥+𝑦 𝑑𝑦𝑑𝑥=𝑎+ 𝑎𝑑𝑦𝑑𝑥 𝑥+𝑦 𝑑𝑦𝑑𝑥=𝑎 1+ 𝑑𝑦𝑑𝑥 a = 𝑥 + 𝑦𝑑𝑦𝑑𝑥 1 + 𝑑𝑦𝑑𝑥 a = 𝑥 + 𝑦 𝑦′1 + 𝑦′ Putting Value of 𝑎 in (1) 𝑥−𝑎2+ 𝑦−𝑎2= 𝑎2 𝑥− 𝑥 + 𝑦 𝑦′1 + 𝑦′2+ 𝑦− 𝑥 + 𝑦 𝑦′1 + 𝑦′2= 𝑥 + 𝑦 𝑦′1 + 𝑦′2 𝑥 1 + 𝑦′− 𝑥 + 𝑦 𝑦′2 1 + 𝑦′2+ 𝑦 1 + 𝑦′− 𝑥 + 𝑦 𝑦′2 1 + 𝑦′2= 𝑥 + 𝑦 𝑦′2 1 + 𝑦′2 𝑥+𝑥 𝑦′−𝑥−𝑦 𝑦′2+ 𝑦+𝑦 𝑦′−𝑥−𝑦 𝑦′2= 𝑥+𝑦 𝑦′2 𝑥 𝑦′−𝑦 𝑦′2+ 𝑦−𝑥2= 𝑥+𝑦 𝑦′2 𝑥−𝑦2 𝑦′2+ 𝑥−𝑦2= 𝑥+𝑦 𝑦′2 𝑥−𝑦2 1+ 𝑦′2= 𝑥+𝑦 𝑦′2 𝒙+𝒚 𝒚′𝟐= 𝒙−𝒚𝟐 𝟏+ 𝒚′𝟐

Chapter 9 Class 12 Differential Equations

Serial order wise

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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .