Asosiy tarkibga o'tish

3.3-bo'lim : Davralar

4. Quyidagi aylananing radiusi va markazini aniqlang va aylananing grafigini chizing.

\[{x^2} + {\left( {y - 5} \right)^2} = 4\]
Yechim

Haqiqatan ham bu muammo uchun juda ko'p narsa yo'q. Aylana radiusi va markazini aniqlash uchun bizga berilgan tenglamani aylananing standart shakli bilan solishtirish kifoya. Malumot uchun bu erda aylananing standart shakli.

\[{\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}\]

Birinchidan, birinchi atamani quyidagicha yozishimiz mumkinligiga e'tibor bering:

\[{x^2} = {\left( {x - 0} \right)^2}\]

va endi biz \(h = 0\)ni ko'rishimiz mumkin

Keyinchalik, ikkinchi muddatdan biz \(k = 5\) ni tezda ko'rishimiz mumkin.

Nihoyat, biz \({r^2} = 4\) ekanligini ko'ramiz va shuning uchun bizda \(r = 2\) bo'lishi kerak.

Shuning uchun aylananing radiusi 2 ga, aylana markazi esa \(\left( {0,5} \right)\) ga teng.

2-qadam

Mana aylananing eskizi.

The graph of the circle with center \(\left( {0,5} \right)\) and radius 2.  The center is marked with a dot and the circle passes through the right most point \(\left( {2,5} \right)\), the left most point \(\left( { - 2,5} \right)\), the top most point \(\left( {0,7} \right)\) and the bottom most point \(\left( {0,3} \right)\).

Esda tutingki, biz tezda markazdan boshlab, so'ngra radius bo'yicha o'ngga/chapga (bu muammo uchun 2) o'ng eng/chap nuqtani olish orqali tezda aylana grafigini tuzishimiz mumkin. Eng yuqori/pastki nuqtani olish uchun biz qilishimiz kerak bo'lgan yagona narsa markazdan boshlash va radius bo'yicha yuqoriga/pastga borish (yana bu muammo uchun 2).