Mehlala ea Lipotso Tse Buisanang ka Boemo ba Ntlha Mabapi le Selikalikoe
Ho fumana boemo ba ntlha e amanang le selikalikoe ke taba ea bohlokoa thutong ea motheo ea jeometri, haholo-holo thutong ea lisekoere. Sehloohong sena, re tla tšohla mehlala e 'maloa ea mathata a amanang le boemo ba ntlha e amanang le selikalikoe, hammoho le litlhaloso tsa bona. Sena se tla thusa ho hlakisa mohopolo ka lits'ebetso tse sebetsang.
Pendahuluan
Pele re teba lipotsong tsa mohlala, a re hopoleng maemo a mararo a ka bang teng a ntlha selikalikoeng:
1. Ka hare ho selikalikoe: Haeba sebaka sa ntlha ho ea bohareng ba selikalikoe se le senyenyane ho feta radius ea selikalikoe.
2. Kantle ho selikalikoe: Haeba sebaka sa ntlha ho ea bohareng ba selikalikoe se le seholo ho feta radius ea selikalikoe.
3. Selikalikoe: Haeba sebaka ho tloha ntlheng ho ea bohareng ba selikalikoe se lekana le radius ea selikalikoe.
Ho ya ka dipalo, boemo ba ntlha \(T(x_1, y_1)\) mabapi le sedikadikwe se bohareng ho \((a, b)\) ka radius \(r\) bo ka fumaneha ka ho bapisa \(T(x_1, y_1)\) le equation ya sedikadikwe, e leng:
\[
(x – a)^2 + (y – b)^2 = r^2
\]
Haeba sephetho sa ho nkela \(x_1\) le \(y_1\) sebakeng sa equation se fana ka boleng:
– E nyane ho feta \(r^2\), ntlha e ka hare ho selikalikoe.
– E kgolo ho feta \(r^2\), ntlha e ka ntle ho sedikadikwe.
– Ho tšoana le \(r^2\), ntlha e holim'a selikalikoe.
Lipotso tsa Mehlala le Puisano
Potso ea 1
Fumana boemo ba ntlha \(T(3, 4)\) mabapi le selikalikoe se nang le equation \((x – 1)^2 + (y – 2)^2 = 25 \).
Puisano:
Mohato oa pele ke ho lekola equation ea selikalikoe le ho fumana sebaka ho tloha ntlheng \(T(3, 4)\) ho ea bohareng ba selikalikoe \((1, 2)\).
1. Hlalosa setsi le radius ea selikalikoe:
Tekanyo ea selikalikoe: \( (x – 1)^2 + (y – 2)^2 = 25 \)
– Bohareng ba selikalikoe (\(a, b\)): (1, 2)
– Radius ea selikalikoe (\(r\)): \(\sqrt{25} = 5\)
2. Bala sebaka se pakeng tsa ntlha \(T(3, 4)\) le bohareng ba selikalikoe \((1, 2)\):
\[
D = \sqrt{(3 – 1)^2 + (4 – 2)^2} = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}
\]
Boleng \( 2\sqrt{2} \hoo e ka bang 2 \makgetlo a 1.414 = 2.828 \) (ka tlase ho \(5\)).
3. Qetello:
Kaha \( 2\sqrt{2} < 5 \), ntlha \( T(3, 4) \) e ka hare ho selikalikoe. Potso ea 2 Selikalikoe se na le setsi ntlheng \( (0, 0) \) le radius ea 7. Fumana boemo ba ntlha \(P(5, 6)\) mabapi le selikalikoe.
Potso ea 3
Fumana boemo ba ntlha \(M(2, -1)\) mabapi le selikalikoe se nang le equation \( x^2 + y^2 = 5 \).
Puisano:
1. Bala sebaka ho tloha ntlha \(M(2, -1)\) ho ea bohareng ba selikalikoe \((0, 0):
\[
D = \sqrt{(2 – 0)^2 + (-1 – 0)^2} = \sqrt{4 + 1} = \sqrt{5}
\]
2. Bapisa sebaka \(D\) le radius ea selikalikoe:
Radius ea selikalikoe (\(r\)) = \(\sqrt{5}\).
3. Qetello:
Kaha \( \sqrt{5} = \sqrt{5} \), ntlha \( M(2, -1) \) e hodima selikalikoe.
Potso ea 4
Selikalikoe se nang le setsi ho \( (4, 3) \) se na le radius \(\sqrt{10}\). Bontsha boemo ba ntlha \( N(7, 7) \) mabapi le selikalikoe sena.
Puisano:
1. Tekanyo ea Selikalikoe:
Tekanyo ea selikalikoe se nang le setsi \( (4, 3) \) le radius \( \sqrt{10} \) ke:
\[
(x – 4)^2 + (y – 3)^2 = 10
\]
2. Bala sebaka ho tloha ntlha \( N(7, 7) \) ho ea bohareng ba selikalikoe \( (4, 3) \):
\[
D = \sqrt{(7 – 4)^2 + (7 – 3)^2} = \ sqrt{3^2 + 4^2} = \ sqrt{9 + 16} = \ sqrt{25} = 5
\]
3. Qetello:
Kaha \( 5 > \sqrt{10} \), ntlha \( N(7, 7) \) e kantle ho selikalikoe.
Ho koala
Ka ho utloisisa mokhoa oa ho bala sebaka sa ntlha ho tloha bohareng ba selikalikoe le ho se bapisa le radius, re ka fumana habonolo boemo ba ntlha mabapi le selikalikoe. Puisano e sehloohong sena e lebelletsoe ho fana ka kutloisiso e hlakileng ea mohopolo le mokhoa oa ho rarolla mathata a amanang le boemo ba ntlha mabapi le selikalikoe.
Ha e le hantle, ho tseba boemo ba lintlha tsena ho molemo haholo lits'ebetsong tse fapaneng tsa lipalo, ho kenyeletsoa tlhahlobo ea jeometri, moralo oa litšoantšo le boenjiniere. Ka hona, ho tseba mohopolo ona hantle ke motheo oa bohlokoa o hlokang tlhokomelo e hlokolosi le kutloisiso e tebileng.
