Misc 5 - Family of circles in first quadrant which touch axes - Formation of Differntial equation when general solution given

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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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 Center of circle = ( , ) Thus, Equation of a circle is 2 + 2 = 2 2 + 2 2 + 2 + 2 2 = 2 2 + 2 2 2 + 2 =0 Since there is only one variable , we differentiate once Differentiating w.r.t. both Sides 2 + 2 2 2 + 2 = 0 2 +2 2 2 +0=0 + = + + = 1+ a = + 1 + a = + 1 + Putting Value of in (1) 2 + 2 = 2 + 1 + 2 + + 1 + 2 = + 1 + 2 1 + + 2 1 + 2 + 1 + + 2 1 + 2 = + 2 1 + 2 + 2 + + 2 = + 2 2 + 2 = + 2 2 2 + 2 = + 2 2 1+ 2 = + 2 + = +

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.