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Last updated at Dec. 10, 2019 by Teachoo
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Ex 9.3, 9 Form the differential equation of the family of hyperbolas having foci on ๐ฅโ๐๐ฅ๐๐ and center at origin. Equation of hyperbola having foci on x-axis & center at origin (0, 0) is ๐ฅ^2/๐^2 โ๐ฆ^2/๐^2 =1 โด Differentiating Both Sides w.r.t. ๐ฅ ๐/๐๐ฅ [๐ฅ^2/๐^2 โ๐ฆ^2/๐^2 ]=๐(1)/๐๐ฅ 1/๐^2 [2๐ฅ]โ1/๐^2 [2๐ฆ . ๐๐ฆ/๐๐ฅ]=0 2๐ฆ/๐^2 . ๐ฆโฒ=2๐ฅ/๐^2 Since it has two variables, we will differentiate twice ๐ฆ/๐^2 ๐ฆโฒ=๐ฅ/๐^2 (๐ฆ/๐ฅ)๐ฆโฒ=๐^2/๐^2 (๐ฆ๐ฆ^โฒ)/๐ฅ = ๐^2/๐^2 Again differentiating both sides w.r.t. x ((๐ฆ๐ฆ^โฒ )^โฒ ๐ฅ โ (๐๐ฅ/๐๐ฅ)(๐ฆ๐ฆ^โฒ ))/๐ฅ^2 =0 (๐ฆ๐ฆ^โฒ )^โฒ ๐ฅ โ (1)(๐ฆ๐ฆ^โฒ )=๐ร๐^๐ (๐ฆ๐ฆ^โฒ )^โฒ ๐ฅ โ๐ฆ๐ฆ^โฒ=๐ (๐๐^โฒ )^โฒ ๐ฅ โ๐ฆ๐ฆ^โฒ=0 (Using Quotient rule and Diff. of constant is 0) (๐^โฒ ๐^โฒ+๐๐โฒโฒ)๐ฅ โ๐ฆ๐ฆ^โฒ=0 (ใ๐ฆ^โฒใ^2+๐ฆ๐ฆโฒโฒ)๐ฅ โ๐ฆ๐ฆ^โฒ=0 ๐ฅใ๐ฆ^โฒใ^2+๐ฅ๐ฆ๐ฆ^โฒโฒโ๐ฆ๐ฆ^โฒ=0 ๐๐๐^โฒโฒ+๐ใ๐^โฒใ^๐โ๐๐^โฒ=๐ (Using Product rule)
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
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 You are here
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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