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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

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 :- (๐‘ฅโˆ’๐‘Ž)^2+(๐‘ฆโˆ’๐‘)^2=๐‘Ÿ^2 Given center is on y-axis โˆด Center = (0, b) And, Radius = 3 Hence, our equation becomes (๐‘ฅโˆ’0)^2+(๐‘ฆโˆ’๐‘)^2=(3)^2 ๐‘ฅ^2+(๐‘ฆโˆ’๐‘)^2=9 Differentiating Both Sides w.r.t. ๐‘ฅ 2๐‘ฅ+2(๐‘ฆโˆ’๐‘)[๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’0]=0 2๐‘ฅ+2(๐‘ฆโˆ’๐‘)๐‘ฆโ€ฒ=0 2[๐‘ฅ+(๐‘ฆโˆ’๐‘)๐‘ฆโ€ฒ]=0 ๐‘ฅ+(๐‘ฆโˆ’๐‘) ๐‘ฆ^โ€ฒ=0 (๐‘ฆโˆ’๐‘)๐‘ฆโ€ฒ=โˆ’๐‘ฅ (๐‘ฆโˆ’๐‘)= (โˆ’๐‘ฅ)/๐‘ฆ^โ€ฒ Putting the value of (๐‘ฆโˆ’๐‘) in equation (1) x2 + (y โˆ’ b)2 = 9 ๐‘ฅ^2+[(โˆ’๐‘ฅ)/๐‘ฆ^โ€ฒ ]^2=9 ๐‘ฅ^2+๐‘ฅ^2/ใ€–๐‘ฆ^โ€ฒใ€—^2 =9 (๐‘ฅ^2 ใ€–๐‘ฆ^โ€ฒใ€—^2+ ๐‘ฅ^2)/ใ€–๐‘ฆ^โ€ฒใ€—^2 =9 ๐‘ฅ^2 ใ€–๐‘ฆ^โ€ฒใ€—^2+๐‘ฅ^2=9ใ€–๐‘ฆ^โ€ฒใ€—^2 ๐‘ฅ^2 ใ€–๐‘ฆ^โ€ฒใ€—^2โˆ’9ใ€–๐‘ฆ^โ€ฒใ€—^2+๐‘ฅ^2=0 ใ€–๐‘ฆ^โ€ฒใ€—^2 (๐‘ฅ^2โˆ’9)+๐‘ฅ^2=0 โˆด (๐’™^๐Ÿโˆ’๐Ÿ—) ใ€–๐’š^โ€ฒใ€—^๐Ÿ+๐’™^๐Ÿ=๐ŸŽ

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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.