# Ex 9.3, 6 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 10, 2019 by Teachoo

Ex 9.3

Ex 9.3, 1
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Ex 9.3, 2 Deleted for CBSE Board 2023 Exams

Ex 9.3, 3 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 4 Deleted for CBSE Board 2023 Exams

Ex 9.3, 5 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 6 Deleted for CBSE Board 2023 Exams You are here

Ex 9.3, 7 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 8 Deleted for CBSE Board 2023 Exams

Ex 9.3, 9 Deleted for CBSE Board 2023 Exams

Ex 9.3, 10 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 11 (MCQ) Deleted for CBSE Board 2023 Exams

Ex 9.3, 12 (MCQ) Important Deleted for CBSE Board 2023 Exams

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at Dec. 10, 2019 by Teachoo

Ex 9.3, 6 Form the differential equation of the family of circle touching the 𝑦−𝑎𝑥𝑖𝑠 at origin. General Equation of Circle (𝑥−𝑎)^2+(𝑦−𝑏)^2=𝑟^2 where Centre at (𝑎 , 𝑏) and Radius is r If circle touches y-axis at origin, Center will be at x-axis So, Center = (a, 0) & Radius = a Thus, equation of circle becomes (𝑥−𝑎)^2+(𝑦−0)^2=𝑎^2 (𝑥−𝑎)^2+𝑦^2=𝑎^2 𝑥^2+𝑎^2−2𝑎𝑥+𝑦^2=𝑎^2 𝑥^2−2𝑎𝑥+𝑦^2=𝑎^2−𝑎^2 𝑥^2−2𝑎𝑥+𝑦^2=0 2𝑎𝑥=𝑥^2+𝑦^2 Differentiating Both Sides w.r.t. 𝑥 (𝑑(2𝑎𝑥))/𝑑𝑥=𝑑(𝑥^2 )/𝑑𝑥+𝑑(𝑦^2 )/𝑑𝑥 2a = 2x + 2y 𝑑𝑦/𝑑𝑥 a = x + yy’ …(1) …(2) From (1) 2𝑎𝑥=𝑥^2+𝑦^2 Putting value of a from (2) 2𝑥(𝑥+𝑦𝑦^′)=𝑥^2+𝑦^2 2𝑥^2+2𝑥𝑦𝑦^′=𝑥^2+𝑦^2 2𝑥^2−𝑥^2+2𝑥𝑦𝑦^′=+𝑦^2 𝟐𝒙𝒚𝒚^′+𝒙^𝟐=𝒚^𝟐 is the required differential equation.