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Ex 9.3, 10 - Family of circle having center on y-axis - Ex 9.3

Ex 9.3, 10 - Chapter 9 Class 12 Differential Equations - Part 2
Ex 9.3, 10 - Chapter 9 Class 12 Differential Equations - Part 3

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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−𝑎)^2+(𝑦−𝑏)^2=𝑟^2 Given center is on y-axis ∴ Center = (0, b) And, Radius = 3 Hence, our equation becomes (𝑥−0)^2+(𝑦−𝑏)^2=(3)^2 𝑥^2+(𝑦−𝑏)^2=9 Differentiating Both Sides w.r.t. 𝑥 2𝑥+2(𝑦−𝑏)[𝑑𝑦/𝑑𝑥−0]=0 2𝑥+2(𝑦−𝑏)𝑦′=0 2[𝑥+(𝑦−𝑏)𝑦′]=0 𝑥+(𝑦−𝑏) 𝑦^′=0 (𝑦−𝑏)𝑦′=−𝑥 (𝑦−𝑏)= (−𝑥)/𝑦^′ Putting the value of (𝑦−𝑏) in equation (1) x2 + (y − b)2 = 9 𝑥^2+[(−𝑥)/𝑦^′ ]^2=9 𝑥^2+𝑥^2/〖𝑦^′〗^2 =9 (𝑥^2 〖𝑦^′〗^2+ 𝑥^2)/〖𝑦^′〗^2 =9 𝑥^2 〖𝑦^′〗^2+𝑥^2=9〖𝑦^′〗^2 𝑥^2 〖𝑦^′〗^2−9〖𝑦^′〗^2+𝑥^2=0 〖𝑦^′〗^2 (𝑥^2−9)+𝑥^2=0 ∴ (𝒙^𝟐−𝟗) 〖𝒚^′〗^𝟐+𝒙^𝟐=𝟎

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.