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Last updated at Dec. 10, 2019 by Teachoo
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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.
Ex 9.3
Ex 9.3, 2 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 3 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 4 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 5 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 6 Not in Syllabus - CBSE Exams 2021 You are here
Ex 9.3, 7 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 8 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 9 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 10 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 11 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 12 Not in Syllabus - CBSE Exams 2021
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