# Ex 9.3, 6 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 10, 2019 by Teachoo

Last updated at Dec. 10, 2019 by Teachoo

Transcript

Ex 9.3, 6 Form the differential equation of the family of circle touching the ๐ฆโ๐๐ฅ๐๐ at origin. General Equation of Circle (๐ฅโ๐)^2+(๐ฆโ๐)^2=๐^2 where Centre at (๐ , ๐) 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 (๐ฅโ๐)^2+(๐ฆโ0)^2=๐^2 (๐ฅโ๐)^2+๐ฆ^2=๐^2 ๐ฅ^2+๐^2โ2๐๐ฅ+๐ฆ^2=๐^2 ๐ฅ^2โ2๐๐ฅ+๐ฆ^2=๐^2โ๐^2 ๐ฅ^2โ2๐๐ฅ+๐ฆ^2=0 2๐๐ฅ=๐ฅ^2+๐ฆ^2 Differentiating Both Sides w.r.t. ๐ฅ (๐(2๐๐ฅ))/๐๐ฅ=๐(๐ฅ^2 )/๐๐ฅ+๐(๐ฆ^2 )/๐๐ฅ 2a = 2x + 2y ๐๐ฆ/๐๐ฅ a = x + yyโ โฆ(1) โฆ(2) From (1) 2๐๐ฅ=๐ฅ^2+๐ฆ^2 Putting value of a from (2) 2๐ฅ(๐ฅ+๐ฆ๐ฆ^โฒ)=๐ฅ^2+๐ฆ^2 2๐ฅ^2+2๐ฅ๐ฆ๐ฆ^โฒ=๐ฅ^2+๐ฆ^2 2๐ฅ^2โ๐ฅ^2+2๐ฅ๐ฆ๐ฆ^โฒ=+๐ฆ^2 ๐๐๐๐^โฒ+๐^๐=๐^๐ is the required differential equation.

Chapter 9 Class 12 Differential Equations

Serial order wise

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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.