Ellips 2 retti zhazyk kisyk Ellips fokus dep atalatyn F1 F2 nүktelerden kashyktyktarynyn kosyndysy birdej bolatyn nүktelerdin zhiyny Tik buryshty koordinattar zhүjesinde Ellips tendeui x2 a2 y2 b2 1 bolady Konusty zhazyktykpen kiganda ellips pajda bolady Ellips elementteri arasyndagy katynastarEllips mүsheleri a displaystyle boldsymbol a үlken zharty osi b displaystyle boldsymbol b kishi zharty osi c displaystyle boldsymbol c fokaldyk radius fokustary arasyndagy zhartylaj kashyktyk p displaystyle boldsymbol p fokaldyk parametri rp displaystyle boldsymbol r p perifokustyk kashyktyk ellipstegi nүkteden fokuska dejingi en zhakyn kashyktyk ra displaystyle boldsymbol r a apofokustyk kashyktyk ellipstegi nүkteden fokuska dejingi en uzyn kashyktyk a2 b2 c2 displaystyle a 2 b 2 c 2 e ca 1 b2a2 0 e lt 1 displaystyle e frac c a sqrt 1 frac b 2 a 2 0 leq e lt 1 p b2a displaystyle p frac b 2 a a displaystyle boldsymbol a b displaystyle boldsymbol b c displaystyle boldsymbol c p displaystyle boldsymbol p rp displaystyle boldsymbol r p ra displaystyle boldsymbol r a a displaystyle boldsymbol a үlken zharty osi a displaystyle boldsymbol a a b1 e2 displaystyle a frac b sqrt 1 e 2 a ce displaystyle a frac c e a p1 e2 displaystyle a frac p 1 e 2 a rp1 e displaystyle a frac r p 1 e a ra1 e displaystyle a frac r a 1 e b displaystyle boldsymbol b kishi zharty osi b a1 e2 displaystyle b a sqrt 1 e 2 b displaystyle boldsymbol b b c 1 e2e displaystyle b frac c sqrt 1 e 2 e b p1 e2 displaystyle b frac p sqrt 1 e 2 b rp1 e1 e displaystyle b r p sqrt frac 1 e 1 e b ra1 e1 e displaystyle b r a sqrt frac 1 e 1 e c displaystyle boldsymbol c fokaldyk kashyktyk c ae displaystyle c ae c be1 e2 displaystyle c frac be sqrt 1 e 2 c displaystyle boldsymbol c c pe1 e2 displaystyle c frac pe 1 e 2 c rpe1 e displaystyle c frac r p e 1 e c rae1 e displaystyle c frac r a e 1 e p displaystyle boldsymbol p fokaldyk parametr p a 1 e2 displaystyle p a 1 e 2 p b 1 e2 displaystyle p b sqrt 1 e 2 p c 1 e2e displaystyle p c frac 1 e 2 e p displaystyle boldsymbol p p rp 1 e displaystyle p r p 1 e p ra 1 e displaystyle p r a 1 e rp displaystyle boldsymbol r p perifokustyk kashyktyk rp a 1 e displaystyle r p a 1 e rp b 1 e1 e displaystyle r p b sqrt frac 1 e 1 e rp c 1 ee displaystyle r p c frac 1 e e rp p1 e displaystyle r p frac p 1 e rp displaystyle boldsymbol r p rp ra1 e1 e displaystyle r p r a frac 1 e 1 e ra displaystyle boldsymbol r a apofokustyk kashyktyk ra a 1 e displaystyle r a a 1 e ra b 1 e1 e displaystyle r a b sqrt frac 1 e 1 e ra c 1 ee displaystyle r a c frac 1 e e ra p1 e displaystyle r a frac p 1 e ra rp 1 e1 e displaystyle r a r p frac 1 e 1 e ra displaystyle boldsymbol r a Koordinattyk tүrde ornekteuEllips ekinshi rettik kisyk retinde Ellips yavlyaetsya centralnoj nevyrozhdennoj zhәne zhalpy myna tendeudi kanagattandyrady a11x2 a22y2 2a12xy 2a13x 2a23y a33 0 displaystyle a 11 x 2 a 22 y 2 2a 12 xy 2a 13 x 2a 23 y a 33 0 invarianttyn D gt 0 displaystyle D gt 0 zhәne DI lt 0 displaystyle Delta I lt 0 bolganda mundagy D a11a12a13a12a22a23a13a23a33 displaystyle Delta begin vmatrix a 11 amp a 12 amp a 13 a 12 amp a 22 amp a 23 a 13 amp a 23 amp a 33 end vmatrix D a11a12a12a22 a11a22 a122 displaystyle D begin vmatrix a 11 amp a 12 a 12 amp a 22 end vmatrix a 11 a 22 a 12 2 I tr a11a12a12a22 a11 a22 displaystyle I tr begin pmatrix a 11 amp a 12 a 12 amp a 22 end pmatrix a 11 a 22 Ekinshi rettik kisyk invarianttary men ellips zharty osteri arasyndagy katynastar D a4b4 displaystyle Delta a 4 b 4 D a2b2 displaystyle D a 2 b 2 I a2 b2 displaystyle I a 2 b 2 DerekkozderRahimbekova Z M Materialdar mehanikasy terminderinin agylshynsha oryssha kazaksha tүsindirme sozdigi ISBN 9965 769 67 2 Қazakstan Ұlttyk enciklopediya Bas redaktor Ә Nysanbaev Almaty Қazak enciklopediyasy Bas redakciyasy 1998 ISBN 5 89800 123 9Bul makalany Uikipediya sapa talaptaryna lajykty boluy үshin uikilendiru kazhet