Hyperbola ndi mphira

Mapangidwe a geometric, otchedwa hyperbola, ndi mpikisano wa ndege wa chiphangachi chachiwiri, chokhala ndi ma curve awiri omwe amakoka mosiyana ndi osagwirizana. Makhalidwe a masamu omwe amafotokozedwa amawoneka monga awa: y = k / x, ngati nambala pansi pa index k si zero. Mwa kuyankhula kwina, mphotho za mphutsi zimakhala zero, koma sizidzalumikizana nazo. Kuchokera pakuwona momwe mfundo yomangidwira, hyperbola ndi chiwerengero cha mfundo pa ndege. Zonsezi ndizomwe zimakhazikika nthawi zonse kusiyana ndi malo awiri.

Mphepete mwachindunji imasiyanitsidwa ndi zikuluzikulu zomwe zimakhalapo zokhazokha:

• Hyperbola ndi mizere iwiri yosiyana, yotchedwa nthambi.
• Pakati pa malo ozungulira kwambiri ndikatikati mwa chiwerengerocho.
• Vertex ndi mfundo za nthambi ziwiri zomwe zimayandikana.
• Mtunda wapatali ndi mtunda wochokera pakatikati pa mphika kupita ku umodzi wa foci (wotchulidwa ndi kalata "c").
• Mtsinje waukulu wa hyperbola umatanthauzira mtunda wautali kwambiri pakati pa nthambi za nthambi.
• Nkhonoyi imakhala pambali yaikulu, motalika kuti mtunda wochokera pakati pa mphikawo ndi wofanana. Mzere umene umagwirizanitsa majekiti akuluakulu amatchedwa "transverse axis".
• The semimajor axis ndi mtunda wowerengedwera kuchokera pakati pa mphukira ku imodzi mwa mawu (otchulidwa ndi kalata "a").
• Mzere wolunjika womwe umayenda mozungulira mpaka kutsogolo kwake kudutsa pakati pawo umatchedwa conjugate axis.
• Cholinga chachikulu chimatanthawuzira gawo pakati pa kuganizira ndi hyperbola podabwitsa kwambiri.
• Mtunda wa pakati pa ganizo ndi aspirote umatchedwa "parameter" ndipo nthawi zambiri amalembedwa m'mawu omwe ali pansi pa kalata "b".

M'zigawo zamakono za Cartesian, chiwerengero chodziwika bwino chimene hyperbola chingamangidwe chikuwoneka ngati ichi: (x ^2/2 ) - (y ² / b ² ) = 1. Mtundu wa mphika umene uli ndi chigawo chimodzi chotchedwa equilateral. Mu njira yokhala ndi makonzedwe ang'onoang'ono, amatha kufotokozera ndi equation equation: xy = 2/2, ndipo zomwe zimaphatikizapo hyperbola ziyenera kupezeka pa mapepala (a, a) ndi (-a, -a).

Kuzungulira kulikonse kungakhale kufanana kwa hyperbola. Ichi ndicho kusiyana kwake kwa conjugate, kumene nsonga zimasintha malo, ndipo zizindikirozo zimakhalabe m'malo. Malo opangidwa ndi chiwonetserochi ndikuti kuunika kuchokera ku gwero lolingalira m'maganizo amodzi kumatha kuwonetsa nthambi yachiwiri ndikuyang'anitsitsa pamaganizidwe achiwiri. Mfundo iliyonse ya hyperbola ikhoza kukhala ndi phindu lokhazikika pa chiwerengero cha mtunda kuti aliyense ayang'anire kutali ndi wotsogolera. Mphepete mwachindunji amatha kusonyeza magalasi ndi kusinthasintha kwapakati pamene amasinthasintha 180 ° pakati.

Kusintha kwa hyperbola kumatsimikiziridwa ndi chiwerengero cha chiwerengero cha conic gawo, zomwe zimasonyeza kukula kwa gawo kuchokera mzere wokongola. Mu ma masamu, chizindikiro ichi chikuwonetsedwa ndi kalata "e". Kusagwedeza kawirikawiri kumakhala kosagwirizana ndi kayendetsedwe ka ndege ndi njira yosinthira kufanana kwake. Hyperbola ndi chifaniziro chomwe nthawi zonse zimakhala zofanana ndi chiŵerengero pakati pa kutalika kwake ndi mzere waukulu.