wngri xngkvs ellipse epnesnokhngthangkhnitsastrsunglxmrxbcudofkssxngcudaelathaihphlrwmkhxngrayathangcakcudbnesnokhngiphacudofksaetlacudepnkhakhngthi cakniyamni wngrithuxepnnythwipkhxngwngklm nnkhux wngklmepnkrniphiesskhxngwngrithimicudofkssxnknepncudediyw khwamyudkhxngwngriaesdngdwykhakhwameyuxngsunyklang sungsahrbwngrixacmikhaidtngaet 0 krniphiesskhxngwngklm aelamakekhaikl 1 ethaidkid aetimthung 1 sungcaklayepnpharaobla wngriyngsamarthniyamepnestkhxngcud thisahrbaetlacudinest xtraswnkhxngrayathangiphacudthikahnd sungcaepnhnungincudofks txrayathangiphaesnthikahnd eriykwaesniderkthriks epnkhakhngthi sungkhakhngthinicaethakbkhwameyuxngsunyklangkhangtnwngrisungmacakkartdkhxngthrngkrwykbranabniyamsxngaebbkhxngwngrisungethiybethakn ichofkssxngcud ekhiyw aelaichofkskbiderkthriks naengin wngriepnphakhtdkrwy nnkhux ekidcakkartdknkhxngthrngkrwykbranab duphaphkhwa aelayngepnphakhtdkhxngthrngkrabxk ykewnechphaakrnithiranabtdkhnankbaeknthrngkrabxkniyamwngrimkniyamepnolkskhxngcudinranabsxngmiti odycakcudofks F1 displaystyle F 1 kb F2 displaystyle F 2 aelarayathang 2a displaystyle 2a caniyamwngriepnestkhxngcud P displaystyle P thnghmdthithaihphlbwkkhxngrayathang PF1 displaystyle PF 1 kb PF2 displaystyle PF 2 epn 2a displaystyle 2a hruxekhiynepnsykrnwa E P R2 PF1 PF2 2a displaystyle E P in mathbb R 2 PF 1 PF 2 2a krnithi 2a F1F2 displaystyle 2a leq F 1 F 2 caldrupepnesntrng dngnnephuxihepnwngricatxngbngkhb 2a gt F1F2 displaystyle 2a gt F 1 F 2 cudkungklangkhxngswnkhxngesntrngechuxmcudofksthngsxng eriykwacudsunyklangkhxngwngri esntrngthiphancudofksthngsxngeriykwaaeknexk aelaesnthiphancudsunyklangaelatngchakkbaeknexkeriykwaaeknoth aeknexktdkbwngklmthicudyxd sunghangcakcudsunyklang a displaystyle a hnwy rayathangcakcudofksipcudsunyklangeriykwarayaofks c displaystyle c xtraswn ca e displaystyle tfrac c a e khuxkhwameyuxngsunyklangsmbtiinrabbphikdkharthiesiyn wngrithimicudsunyklangthi h k displaystyle h k aeknexkkhnanaekn x yaw 2a displaystyle 2a aeknothkhnanaekn y yaw 2b displaystyle 2b ekhiynsmkaridepn x h 2a2 y k 2b2 1 displaystyle frac x h 2 a 2 frac y k 2 b 2 1 khwameyuxngsunyklangkhxngwngriepniptamsutr e 1 ba 2 displaystyle e sqrt 1 left frac b a right 2 hakichrabbsmkarxingtwaepresrim casamarthekhiynwngriinrupkhxngfngkchntrioknmitiepn x h acos t y k bsin t 0 t lt 2p displaystyle x h a cos t y k b sin t 0 leq t lt 2 pi hakaethn u tan t 2 displaystyle u tan t 2 caidsmkartwaepresrimxikrupkhux x h a 1 u21 u2 y k b 2u1 u2 lt u lt displaystyle x h a left frac 1 u 2 1 u 2 right y k b left frac 2u 1 u 2 right infty lt u lt infty inphikdechingkhw hakichcudsunyklangkhxngwngriepncudkaenid aelawdmumethiybkbaeknexk caidepnsmkar r 8 ab bcos 8 2 asin 8 2 b1 ecos 8 2 displaystyle r theta frac ab sqrt b cos theta 2 a sin theta 2 frac b sqrt 1 e cos theta 2 aethakichcudofksepncudkaenid caidsmkarthingaykwa khux r 8 a 1 e2 1 ecos 8 displaystyle r theta frac a 1 e 2 1 pm e cos theta wngrimiphunthi pab displaystyle pi ab ehnidcakkarmxngwngriepnwngklmrsmi b displaystyle b thithukyudxxk a b displaystyle a b etha cungidphunthiepn pb2 ab pab displaystyle pi b 2 frac a b pi ab hruxxacphisucncakkarxinthiekrt odycdrupsmkarwngri x2a2 y2b2 1 displaystyle frac x 2 a 2 frac y 2 b 2 1 epn y b1 x2 a2 displaystyle y b sqrt 1 x 2 a 2 xinthiekrtcak a displaystyle a thung a displaystyle a caidphunthikhrungbn dngnnidepn A 2 aab1 x2a2 dx ba 2 aaa2 x2 dx ba pa2 pab displaystyle begin aligned A amp 2 int a a b sqrt 1 frac x 2 a 2 dx amp frac b a cdot 2 int a a sqrt a 2 x 2 dx amp frac b a cdot pi a 2 amp pi ab end aligned khwamyawrxbrupkhxngwngriimsamarthekhiynepnsutrxyangngayid odymikhaethakbxinthikrl C 4a 0p 21 e2sin2 8 d8 4aE e displaystyle C 4a int 0 pi 2 sqrt 1 e 2 sin 2 theta d theta 4aE e emux E displaystyle E epnpriphnthwngrismburnchnidthisxng Complete elliptic integral of the second kind E e 0p 21 e2sin2 8 d8 displaystyle E e int 0 pi 2 sqrt 1 e 2 sin 2 theta d theta sutrkhwamyawrxbrupsamarthekhiyninrupxnukrmxnntidepn C 2pa 1 12 2e2 1 32 4 2e43 1 3 52 4 6 2e65 2pa 1 n 1 2n 1 2n 2e2n2n 1 displaystyle begin aligned C amp 2 pi a left 1 left frac 1 2 right 2 e 2 left frac 1 cdot 3 2 cdot 4 right 2 frac e 4 3 left frac 1 cdot 3 cdot 5 2 cdot 4 cdot 6 right 2 frac e 6 5 cdots right amp 2 pi a left 1 sum n 1 infty left frac 2n 1 2n right 2 frac e 2n 2n 1 right end aligned ramanucnidihsutrpramankhakhwamyawrxbrupwa C p 3 a b 3a b a 3b p 3 a b 10ab 3 a2 b2 displaystyle C approx pi left 3 a b sqrt 3a b a 3b right pi left 3 a b sqrt 10ab 3 a 2 b 2 right bthkhwamerkhakhnitniyngepnokhrng khunsamarthchwywikiphiediyidodykarephimetimkhxmuldk, wikipedia, แบบไทย, วิกิพีเดีย, วิกิ หนังสือ, หนังสือ, ห้องสมุด, บทความ, อ่าน, ดาวน์โหลด, ฟรี, ดาวน์โหลดฟรี, mp3, วิดีโอ, mp4, 3gp, jpg, jpeg, gif, png, รูปภาพ, เพลง, เพลง, หนัง, หนังสือ, เกม, เกม, มือถือ, โทรศัพท์, Android, iOS, Apple, โทรศัพท์โมบิล, Samsung, iPhone, Xiomi, Xiaomi, Redmi, Honor, Oppo, Nokia, Sonya, MI, PC, พีซี, web, เว็บ, คอมพิวเตอร์