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Geometre homework2
1.
Бие даалт (Геометр
2) 1. 9x2 +36y2 =144 Эллипсийн фокусууд, тэнхлэгүүд, эксцентристетийг ол. 2. Бага тэнхлэг нь 6, эксцентристет нь 0,8 байх эллипсийн тэгшитгэлийг бич. 3. 5x2 +2y2 =5 Эллипсийн фокусууд, тэнхлэгүүд, эксцентристетийг ол. 4. x2 -9y2 =441 гиперболийн фокусууд, бодит ба хуурмаг тэнхлэгүүд, эксцентристетийг ол. 5. Эллипсийн фокусуудын хоорондох зай нь дээд орой ба зүүн оройн хоорондох зайтай тэнцүү бол эксцентристетийг ол. 6. 25x2 +30y2 =750 Эллипсийн директрисүүдийн тэгшитгэлийг бич. 7. x2 -2y2 =5 гиперболийн фокусууд, бодит ба хуурмаг тэнхлэгүүд, эксцентристетийг ол.Асимптотын тэгшитгэлийг бич. 8. Гиперболын бодит тэнхлэг 16, асимптотын өнцгийн коэффицент 4 3 бол тэгшитгэлийг бич. 9. Гиперболын фокусуудын хоорондох зай 22 ,эксцентрестит 2 бол гиперболын тэгшитгэлийг бич. 10. 1 25625 22 =− yx гиперболын фокусуудыг ол. 11. Гиперболын фокусыг дайрсан бөгөөд бодит тэнхлэгт перпендикуляр хөвчийн уртыг ол. 12. 1 916 22 =− yx гипербол дээр орших Т цэгээс координатын эх хүртэлх зай 544 бол Т цэгийг ол. 13. 1 2449 22 =+ yx эллипстэй ерөнхий фокус бүхий гиперболын эксцентрестит 4 5 бол гиперболын тэгшитгэлийг бич. 14. Ох тэнхлэгийн хувьд тэгш хэмтэй бөгөөд координатын эхийг дайрсан параболын фокус нь А(0,2) цэгийг дайрах бол параболын тэгшитгэлийг бич. 15. Ох тэнхлэгийн хувьд тэгш хэмтэй парабол нь А(2,4) цэгийг дайрах бол параболын тэгшитгэлийг бич. 16. Y2 =18x Парабол ба 9x-12y+40=0 шулууны огтлолын цэгийг ол. 17. Y2 =18x Парабол ба (x+6)2 + y2 =100 тойрог хоёрын ерөнхий хөвчийн тэгшитгэлийг бич. 18. m–ийн ямар утганд mxy −= 2 5 шулуун ба 1 169 22 =− yx гипербол хоёр а). Огтолцох б). Шүргэлцэх в).огтолцохгүй вэ 19. m–ийн ямар утганд mxy += 2 5 шулуун ба 1 3649 22 =+ yx эллипс хоёр а. Огтолцох б. Шүргэлцэх в.огтолцохгүй вэ
2.
20. Эллипсийн фокусуудын
хоорондох зай нь дээд орой ба зүүн оройн хоорондох зайтай тэнцүү бол эксцентристетийг ол. 21. B(20,-9) цэгийг дайрах гиперболын нэг асимптот нь D(-8,-6) цэгийг дайрах бол тэгшитгэлийг бич. 22. M(1,-1) цэгийг дайрах эллипсийн эксцентрестит 5 3 бол эллипсийн тэгшитгэлийг бич. 23. x2 + y2 =16 ба (x-5)2 + y2 =9 тойрог хоёрын ерөнхий хөвчийн тэгшитгэлийг бич. 24. Хэрэв эллипсийн бага тэнхлэг нь фокусаас тэгш өнцгөөр харагдах бол эксцентреститийг ол. 25. Ох тэнхлэгийн хувьд тэгш хэмтэй бөгөөд координатын эхийг дайрсан парабол нь y=2x шулууныг 22 урттай хөвчөөр огтолсон бол параболын тэгшитгэлийг бич. 26. Дэлхий нарыг эллипс замаар тойрох ба нэг фокус дээр нар оршино. Дэлхий наранд ойртох хамгийн бага зай 147,5 сая км, хамгийн холдох зай 152,5 сая км бол дэлхийн тойрог замын тэгшитгэлийг бич. Их хагас тэнхлэг, эксцентристетийг ол. 27. Гиперболын асимптотын хоорондох өнцөг 6 π бол эксцентристетийг ол. 28. Гиперболын асимптотын хоорондох өнцөг 6 π ба B( 6 ,- 2 ) цэгийг дайрах бол тэгшитгэлийг бич. 29. Тойргийг төв нь x+y=3 шулуун дээр орших ба тойрог A(4,2), B(1,5) цэгүүдийг дайрах бол тойргийн тэгшитгэлийг бич. 30. X-4y=12 шулууны (x-2)2 + (y+2)2 =16 тойрогын дотор орших хөвчийн дундаж цэгийг дайрах диаметрын тэгшитгэлийг бич. II эрэмбийн муруйг хялбарчилж, муруйг зур. 1 y=4x*x-8x+7 26 x*x-6x+8=0 2 4x*x+9y*y-8x-36y+4=0 27 x*x+2x+5=0 3 xy-x+2y=6 28 14x*x+24xy+21y*y-4x+18y-139=0 4 3x*x+2xy+y*y-4x-4y=0 29 4xy+3y*y+16x+12y-36=0 5 y=4x*x-8x+7 30 9x*x-24xy+16y*y-20x+110y-50=0 6 2x*x=-y 31 16y*y+25x*x-32y+50x-359=0 7 x+4y*y=0 32 y*y/4-x*x/9-y-2x/3-1=0 8 8xy=1 33 y*y+4x*x-4y-8x+8=0 9 9xy=13 34 y*y-x*x-6y+10=0 10 5xy+6=0 35 2y*y-4y+2x-3=0
3.
11 2xy=1 36
y*y-6y+8=0 12 2x*x-4x=y 37 y*y+2y+5=0 13 x*x-2x-2+y=0 38 14y*y+24xy+21x*x-4y+18x-139=0 14 4y*y-y+x=0 39 4xy+3x*x+16y+12x-36=0 15 y*y+4y-x+5=0 40 9y*y-24xy+16x*x-20y+110x-50=0 16 4xy-y-2x=0 41 x*x+y*y-4y-6x=0 17 3xy-2y-2x-=0 42 9x*x+24xy+16y*y-40y+30x=0 18 5xy+4y-10x-2=0 43 5x*x+6xy+5y*y+16y+16x-16=0 19 2xy+y-x-3=0 44 x*x-8xy+7y*y+6y-6x+9=0 20 36x*x+36y*y-36x-24y-23=0 45 5x*x+4xy+8y*y-16y-28x+80=0 21 16x*x+25y*y-32x+50y- 359=0 46 x*x-3y*y+18x-6y-6=0 22 x*x/4-y*y/9-x-2y/3-1=0 47 x*x-8x-8y=0 23 x*x+4y*y-4x-8y+8=0 48 x*x+6x-4y+1=0 24 x*x-y*y-6x+10=0 49 9x*x-25y*y+150x+36y-289=0 25 2x*x-4x+2y-3=0 50 36x*x+4y*y+8x-72y-104=0
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