Mohlala oa Potso ea Puisano mabapi le Tekanyo ea Selikalikoe
Tekanyo ea selikalikoe ke sehlooho sa bohlokoa thutong ea jeometri ea tlhahlobo. Kutloisiso e ntle ea tekanyo ea selikalikoe e molemo haholo, eseng feela lipalo empa hape le lits'ebetsong tse fapaneng tsa boenjiniere le saense. Sehloohong sena, re tla tšohla mehlala e 'maloa ea li-equation tsa selikalikoe le litharollo tsa tsona. Sepheo ke ho fana ka kakaretso e hlakileng le e felletseng ea mokhoa oa ho rarolla mathata a amanang le li-equation tsa selikalikoe.
Tekanyo e Akaretsang ea Selikalikoe
Tekanyo e tloaelehileng haholo ea selikalikoe ho li-coordinate tsa Cartesian ke:
\[ (x – a)^2 + (y – b)^2 = r^2 \]
Di mana:
– \( (a, b) \) ke dikhokahano tsa bohareng ba sedikadikwe.
– \( r \) ke radius ya sedikadikwe.
Haeba setsi sa selikalikoe se le ntlheng \( (0, 0) \), equation ea selikalikoe e tla ba:
\[ x^2 + y^2 = r^2 \]
Jwale, ha re buisaneng ka mehlala ya dipotso le ditharollo tsa tsona.
Mohlala oa Potso ea 1
Potso: Fumana equation ea selikalikoe seo setsi sa sona se leng ntlheng (3, -2) 'me se na le radius ea 5.
Tharollo:
Sebelisa foromo e akaretsang bakeng sa equation ea selikalikoe:
\[ (x – a)^2 + (y – b)^2 = r^2 \]
Kenya boleng sebakeng sa bona \( a = 3 \), \( b = -2 \), le \( r = 5 \):
\[ (x – 3)^2 + (y + 2)^2 = 5^2 \]
\[ (x – 3)^2 + (y + 2)^2 = 25 \]
Kahoo, equation ea selikalikoe ke:
\[ (x – 3)^2 + (y + 2)^2 = 25 \]
Mohlala oa Potso ea 2
Potso: Fumana equation ea selikalikoe seo setsi sa sona se leng qalong (0, 0) 'me se na le radius ea 7.
Tharollo:
Kaha setsi sa selikalikoe se qalong, re ka sebelisa equation e bonolo:
\[ x^2 + y^2 = r^2 \]
Kenya boleng ba \(r = 7 \):
\[ x^2 + y^2 = 7^2 \]
\[ x^2 + y^2 = 49 \]
Kahoo, equation ea selikalikoe ke:
\[ x^2 + y^2 = 49 \]
Mohlala oa Potso ea 3
Potso: Fumana equation ea selikalikoe seo setsi sa sona se leng ntlheng (4, -5) 'me se ama mothapo oa Y.
Tharollo:
Selikalikoe se potileng mothapong oa Y se bolela hore sebaka se tlohang bohareng ba selikalikoe ho ea mothapong oa Y se lekana le radius ea sona. Sebaka sena ke boleng bo felletseng ba X-coordinate ea setsi sa selikalikoe. Kahoo, radius ke 4.
Sebelisa foromo e akaretsang bakeng sa equation ea selikalikoe:
\[ (x – a)^2 + (y – b)^2 = r^2 \]
Kenya boleng sebakeng sa bona \( a = 4 \), \( b = -5 \), le \( r = 4 \):
\[ (x – 4)^2 + (y + 5)^2 = 4^2 \]
\[ (x – 4)^2 + (y + 5)^2 = 16 \]
Kahoo, equation ea selikalikoe ke:
\[ (x – 4)^2 + (y + 5)^2 = 16 \]
Mohlala oa Potso ea 4
Potso: Selikalikoe se na le equation \( x^2 + y^2 – 6x + 4y – 12 = 0 \). Fumana setsi le radius ea selikalikoe.
Tharollo:
Ho rarolla equation ena, re hloka ho e fetolela ho foromo e tloaelehileng \( (x – a)^2 + (y – b)^2 = r^2 \). Mehato ea ho e tlatsa ke e latelang:
1. Ho hlopha le ho rarolla dikwere tse phethahetseng:
Tekanyo ea pele ke:
\[ x^2 + y^2 – 6x + 4y – 12 = 0 \]
Sehlopha \( x \) le \( y \):
\[ (x^2 – 6x) + (y^2 + 4y) = 12 \]
2. Rarolla sekwere se phethahetseng:
Bakeng sa \( x^2 – 6x \):
\[x^2 – 6x + 9 \]
Bakeng sa \( y^2 + 4y \):
\[ y^2 + 4y + 4 \]
Kenya 9 le 4 mahlakoreng ka bobeli a equation:
\[ (x^2 – 6x + 9) + (y^2 + 4y + 4) = 12 + 9 + 4 \]
\[ (x – 3)^2 + (y + 2)^2 = 25 \]
Kahoo, equation ea selikalikoe ka mokhoa o tloaelehileng ke:
\[ (x – 3)^2 + (y + 2)^2 = 25 \]
Ho tloha mona, re ka bona hore setsi sa selikalikoe ke \( (3, -2) \) mme radius ke \( r = \sqrt{25} = 5 \).
Mohlala oa Potso ea 5
Potso: Fumana equation ea selikalikoe se fetang lintlheng (2, 3) le (4, 5), 'me setsi sa eona se moleng oa x = 3.
Tharollo:
Ho tsoa potsong, rea tseba hore bohareng ba selikalikoe ke (3, b). Selikalikoe le sona se feta lintlheng tse peli tse tsejoang. Kaha selikalikoe se feta (2, 3), sebaka se tlohang bohareng ho ea ntlheng ena ke radius.
Tekanyo ea selikalikoe ke:
\[ (x – 3)^2 + (y – b)^2 = r^2 \]
Ntlha ea ho nkela sebaka (2, 3):
\[ (2 – 3)^2 + (3 – b)^2 = r^2 \]
\[ 1 + (3 – b)^2 = r^2 \]
\[ (3 – b)^2 = r^2 – 1 \]
Ntlha ea ho nkela sebaka (4, 5):
\[ (4 – 3)^2 + (5 – b)^2 = r^2 \]
\[ 1 + (5 – b)^2 = r^2 \]
\[ (5 – b)^2 = r^2 – 1 \]
Ho tsoa ho diekabone tse pedi, re tseba (3 – b)^2 = (5 – b)^2. Kahoo:
\[ 3 – b = \pm(5 – b) \]
Haeba \( 3 – b = 5 – b \), sephetho e ke ke ea e-ba 'nete. Kahoo:
\[ 3 – b = -(5 – b) \]
\[b = 4 \]
Ka b = 4, equation ea selikalikoe ke:
\[ (x – 3)^2 + (y – 4)^2 = 2 \]
Leha ho le jwalo, re ka bala radius r ho tloha sebakeng se pakeng tsa setsi le ntlha (2, 3) = \(\sqrt{(2 – 3)^2 + (3 – 4)^2} \) = \(\sqrt{1+1}\) = \(\sqrt {2}\)
Tekanyo ea selikalikoe ke:
\[ (x – 3)^2 + (y – 4)^2 = 2 \]
Qetello
Ho utloisisa equation ea selikalikoe ho ka nolofatsa ho rarolla mathata a mangata a lipalo. Tabeng ka 'ngoe, ho khetholla setsi le radius ho bohlokoa. Re tšepa hore mehlala ena ea mathata le litlhaloso tsa 'ona li tla u hlakisa le ho u thusa ho ithuta equation ea selikalikoe. Ho itlhakisa ho etsa hore lipalo li phethahale, kahoo u se ke ua tsilatsila ho leka mathata a fapaneng ho ntlafatsa tsebo ea hau.
