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1-Find-the-equation-of-hyperbola-with-centre-point-at-1-2-and-coordinates-of-foci-is-6-2-and-4-2-2-If-hyperbola-x-2-2nx-n-2-25-y-2-2my-m-2-16-1-have-a-asympyotes-passes-t




Question Number 112159 by bobhans last updated on 06/Sep/20
(1)Find the equation of hyperbola with   centre point at (1,−2) and coordinates  of foci is (6,−2) and (−4,−2)  (2) If hyperbola ((x^2 −2nx+n^2 )/(25))−((y^2 −2my+m^2 )/(16))=1  have a asympyotes passes through at   (0,1), then 5m−4n =
(1)Findtheequationofhyperbolawithcentrepointat(1,2)andcoordinatesoffociis(6,2)and(4,2)(2)Ifhyperbolax22nx+n225y22my+m216=1haveaasympyotespassesthroughat(0,1),then5m4n=
Answered by bemath last updated on 06/Sep/20
(2) (((x−n)^2 )/5^2 )−(((y−m)^2 )/4^2 )=1→ asymptotes y−m = ± (4/5)(x−n)  passes through (0,1) →1−m=±(4/5)(−n)  →5−5m = ∓ 4n ; 5m∓ 4n = 5
(2)(xn)252(ym)242=1asymptotesym=±45(xn)passesthrough(0,1)1m=±45(n)55m=4n;5m4n=5

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