ikkinchi tartibli chiziqlar ellips, giperbolava parabola. ularning kanonik tenglamalari

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1629118702.doc r d e f = + - 2 2 10 mf x c y mf x c y 1 2 2 2 2 2 = + + = - + ( ) ( ) ( ) ( ) x c y x c y a + + + - + = 2 2 2 2 2 ó m(x,y) 0 x f 1 ( - c:0) f 2 (c:0) ( ) ( ) x c y a x c y + + = - - + 2 2 2 2 2 ( ) ( ) ( ) x c y a x c y a x c y + + = + - + - - + 2 2 2 2 2 2 2 4 4 a x c y a cx ( ) - + = - 2 2 2 2 a x a y b 2 2 2 …

) òåíãëàìà qóéèäàãè êo’ðèíèøíè îëàäè: (x+d)2+(y+e)2=0 áó òåíãëàìàíè ôàqàò (-d,-e) íóqòà êîîðäèíàòàëàðèãèíà qàíoàòlantèðàäè. 3) d2+e2-f 2c. äåêàðò êîîðäèíàòàëàð ñèñòåìàñèíè îëàìèç. òàíëàá îëãàí êîîðdèíàòàëàð ñèñòåìàñèäà ÷àï ôîêóñ f1(-c:0) âà o’íã ôîêóñ f2(c:0), 1-rasmäàí ì(õ, ó) èõòè¸ðèé íóqòà. ýëëèïñ òåíãëàìàñèíè êåëòèðèá ÷èqàðàìèç. (4) ãà àñîñàí (5) 1-rasm. òåíãëàìàíè ñîääàëàøòèðèø ó÷óí þqîðèäàãè èôîäàíè qóéèäàãè÷à ¸çàìèç. òåíãëàìàíè èêêàëà òîìîíèíè êâàäðàòãà êo’òàðñàê sîääàëàøòèðãàíäàí ño’íã ÿíà êâàäðàòãà êo’òàðñàê [(õ-ñ)2+ó2]=à4-2à2ñõ+ñ2õ2 âà ñîääàëàøòèðñàê (à2-ñ2)õ2+à2ó2=à2(à2-ñ2) à2-ñ2 ìóñáàò ñîí, øóíèíã ó÷óí à2-ñ2=b2 äåá îëñàê (5) òåíãëàìà qóéèäàãè÷à êo’ðèíèøãà êåëàäè (6) ýëëèïñíè èõòè¸ðèé íóqòàëàðè (6) òåíãëàìàíè qàíîàòëàíòèðàäè, (6) ýëëèïñíèíã êàíîíèê òåíãëàìàñè äåéèëàäè. ýíäè ýëëèïñíèíã êàíîíèê òåíãëàìàñèäàí ôîéäàëàíèá óíèíã øàêëèíè òåêøèðàìèç. (6) òåíãëàìàãà ýëëèïñíèíã õ âà ó íèíã êâàäðàòëàðèãèíà êèðàäè, øó ñàáàáëè (õ, ó) íóqòà ýëëèïñíèíã íóqòàñè áo’ëcà, ((õ, (ó) íóqòà õàì ýëëèïñíèíã íóqòàñè áo’ëàäè. øóíäàé êo’ðèíèødà ýëëèïñ êîîðäèíàòà o’qëàðèãà íèñáàòàí ñèììåòðèê æîéëàøãàí, øóíèíã ó÷óí ýëëèïñ øàêëèíè áèðèí÷è chorakäà òåêøèðèø êèôîÿ. (6) òåíãëàìàíè ó ãà íèñáàòàí å÷àìèç. (7) ó õàqèqèé ñîí áo’ëèøè …

’qëàðè äåéèëàäè (à>b áo’ëèøè øàðò). (6) òåíãëàìàäà à=b äåá îëèíñà, õ2+ó2=à2 êo’ðèíèøèãà ýãà áo’ëàäè. áó òåíãëàìà ðàäèóñè à ãà òåíã áo’ëãàí àéëàíàíèíã òåíãëàìàñèäèð. ýëëèïñíèíã ýêñöåíòðèñèòåòè. ýëëèïñíèíã ôîêóñëàðè îðàñèäàãè ìàñîôàíè óíèíã êàòòà o’qè óçóíëèãèãà íèñáàòè ýëëèïñíèíã ýêñöåíòðèñèòåòè äåéèëàäè âà deá belgilanadè. ñ íîëäàí à ãà÷à áo’ëãàí qèéìàòëàðíè îëèø ìóìêèí, øóíèíã ó÷óí 0(( , à áóíäà (>1 ýêñöåíòðèñèòåòè ãèïåðáîëàíè ôîðìàñèíè èôîäàëàéäè ñ2=à2-b2 äàí . äåìàê ýêñöåíòðèñèòåòè êè÷èê áo’ëãàí ñàðè o’qëàðíèíã ìuíîñàáàòëàðè b/à õàì êàì áo’ëàäè. àãàð à o’çãàðìàé qîëèá b êàòòàëàøèá áîðñà ãèïåðáîëàíèíã ýêñöåíòðèñèòåòè 1 äàí àí÷à êàòòà qèéìàòëàð qàáóë qèëàäè âà áó õîëäà ãèïåðáîëà øîõëàðè êåíãàéèá áîðàäè ( 1 ãà qàí÷à ÿqèí áo’ëñà ãèïåðáîëàíèíã øîõëàðè øóí÷à ñèëëèq âà ( 1 äàí qàí÷à êàòòà áo’ëñà ãèïåðáîëà øîõëàðè øóí÷à ¸éèq áo’ëàäè. ìèñîë 1. ôîêóñëàð îðàñèäàãè ìàñîôà 16 ýêñöåíòðèñèòåòè 8/7 áo’ëãàí ãèïåðáîëàíèíã êàíîíèê òåíãëàìàñè òóçèëñèí. å÷èø. øàðò áo’éè÷à 2ñ=16, ñ=8, (=ñ/à=8/7 äåìàê , v= ãèïåðáîëàíèíã êàíîíèê òåíãëàìàñè qóéèäàãè÷à áo’ëàäè . ìèñîë 2. m1(-3; ) …

àðàáîëàíèíã øàêëèäàãèãà íèñáàòàí òåñêàðè á¢ëàäè. àãàð ïàðàáîëàíèíã (13) òåíãëàìàñèäà õ âà ó ¢ðèíëàðèíè àëìàøòèðñàê, ÿúíè õ2=2ðó ê¢ðèíèøíè îëàäè âà êîîðäèíàòà ¢qëàðèãà íèñáàòàí qóéèäàãè÷à æîéëàøãàí á¢ëàäè. ïàðàáîëàíèíã ýêñöåíòðèñèòåòè âà äèðåêòðèñàñè. ïàðàáîëàíèíã è�òè¸ðèé íóqòàñèäàí óíèíã ôîêóñãà÷à á¢ëãàí ìàñîôàíè r1 áèëàí äèðåêòðèñàñèãà÷à á¢ëãàí ìàñîôàíè d áèëàí áåëãèëàá, ïàðàáîëà òàúðèôèäàí r=d áóíäàé r/d=1 øóíèíã ó÷óí ïàðàáîëà ýêñöåíòðèñèòåòè ( = 1 (2) òåíãëàìà ó÷óí äèðåêòðèñà òåíãëàìàñè õ=-ð/2 ìèñîë 1. îõ ¢q ïàðàáîëàíèíã ñèììåòðèÿ ¢qè, óíè ó÷è êîîðäèíàòàëàð áîøèäà ¸òàäè, ïàðàáîëà ôîêóñèäàí ó÷èãà÷à á¢ëãàí ìàñîôà 4 áèðëèêêà òåíã. ïàðàáîëà òåíãëàìàñè òóçèëñèí. å÷èø. ìàñàëàíèíã øàðòèãà àñîñàí, ïàðàáîëàíèíã òåíãëàìàñè ó2=2ðõ á¢ëàäè. îf=4 ð/2=4 ¸êè ð=8 áó qèéìàòíè ïàðàáîëà òåíãëàìàñèãà q¢éñàê ó2=16õ. ìèñîë 2. ïàðàáîëà òåíãëàìàñè áåðèëãàí ó2=6õ. óíèíã ôîêóñèíè koordinatalarini âà äèråêòðèñàñèni òåíãëàìàñèíè òóçèíã. å÷èø. áó åðäà 2ð=6, ð=3 äèðåêòðèñà òåíãëàìàñè õ=-ð/2 õ=-3/2 ôîêóñè f(3/2; 0). _1025792000.unknown _1025792020.unknown _1026158417.unknown _1077284171.doc _1124621738.doc _1124621897.doc _1124622007.doc _1077284218.unknown _1077284293.doc _1077284215.unknown _1026159168.unknown _1037452581.doc _1077284065.unknown _1026159171.unknown _1037452247.doc _1026159169.unknown _1026158904.unknown _1026159167.unknown _1026158488.unknown _1026158180.unknown _1026158261.unknown _1026158297.unknown …

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"ikkinchi tartibli chiziqlar ellips, giperbolava parabola. ularning kanonik tenglamalari" haqida

1629118702.doc r d e f = + - 2 2 10 mf x c y mf x c y 1 2 2 2 2 2 = + + = - + ( ) ( ) ( ) ( ) x c y x c y a + + + - + = 2 2 2 2 2 ó m(x,y) 0 x f 1 ( - c:0) f 2 (c:0) ( ) ( ) x c y a x c y + + = - - + 2 2 2 2 2 ( ) ( ) ( ) x c y a x c y a x c y + + = + - + - - + 2 2 2 …

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