Lipotso tsa Mehlala le Puisano ea Likarolo tsa Parabolic Conic
Likarolo tsa Conic ke sehlooho sa bohlokoa thutong ea jeometri, se akaretsang libopeho tse fapaneng tse kang li-circles, li-ellipses, li-hyperbolas le li-parabolas. E 'ngoe ea libopeho tse hlahelletseng le tse buuoang khafetsa ke parabola. Li-parabolas li na le lits'ebeliso tse ngata lipalo tsa thuto le bophelong ba letsatsi le letsatsi, joalo ka moralo oa lijana tsa sathelaete le li-reflector tsa mabone a koloi.
Ho utloisisa Parabola
Parabola e ka hlalosoa e le sebaka sa lintlha tse hole ka ho lekana le ntlha e tsitsitseng e bitsoang focus le mola o tsitsitseng o bitsoang directrix. Haeba re nahana ka parabola tsamaisong ea Cartesian coordinate, joale tlhokomelo e ho x- kapa y-axis, ho latela tataiso ea parabola.
Ka kakaretso, li-equation tse tloaelehileng tsa parabola ke:
– \( y^2 = 4ax \) bakeng sa parabola e shebileng ka ho le letona kapa ka ho le letshehadi.
– \( x^2 = 4day \) bakeng sa parabola e shebileng holimo kapa tlase.
Mohlala oa Mathata a Karolo ea Parabolic Conic
Mehlala e meng ea lipotso tse amanang le parabola le lipuisano tsa tsona ke ena.
Mohlala oa Potso ea 1: Ho Fumana Tsepamiso le Directrix
Potso:
Ha ho fanoe ka equation ea parabola \( y^2 = 8x \). Fumana likhokahano tsa focus le equation ea directrix.
Puisano:
Ho tsoa ho equation \( y^2 = 8x \), re ka ngola hore parabola ena e na le sebopeho \( y^2 = 4ax \) le \( 4a = 8 \) e le hore \( a = 2 \).
– Lihokelo tsa ho tsepamisa maikutlo: Sepheo sa parabola se supang ka ho le letona (\( y^2 = 4ax \)) se ntlheng \((a, 0)\) kapa \((2, 0)\).
– Tekanyo ea Directrix: Tekanyo ea Directrix ea parabola ena ke mola o otlolohileng o nang le equation \( x = -a \) kapa \( x = -2 \).
Kahoo, likhokahano tsa ho tsepamisa maikutlo tsa parabola \( y^2 = 8x \) ke \((2, 0)\) mme equation ya directrix ke \( x = -2 \).
Mohlala oa Potso ea 2: Ho Fumana Tekanyo ea Parabola ho tsoa ho Focus le Directrix
Potso:
Sepheo sa parabola ke \( (3, 0) \) mme directrix ke \( x = -3 \). Fumana equation ya parabola.
Puisano:
Ka ho tseba ho tsepamisa maikutlo \( (3, 0) \) le directrix \( x = -3 \), re ka fumana boleng ba \( a \) ho tsoa kamanong e pakeng tsa ho tsepamisa maikutlo le directrix.
– Sebaka ho tloha ho tsepamisa maikutlo ho ya ho y-axis (0) ke \( 3 \).
– Sena se bolela hore, sebaka se pakeng tsa ho tsepamisa maikutlo le directrix ke \( 2a = 3 + 3\), kahoo \( 2a = 6 \), ebe \( a = 3 \).
Sebopeho se akaretsang sa parabola e shebileng ka letsohong le letona ke \( y^2 = 4ax \).
Ka \( a = 3 \), re e nkela sebaka ka equation ea parabola:
\[ y^2 = 4(3)x \]
\[ y^2 = 12x \]
Kahoo, equation ea parabola eo sepheo sa eona e leng \( (3, 0) \) le eo directrix ea eona e leng \( x = -3 \) ke \( y^2 = 12x \).
Mohlala oa Potso ea 3: Ho Bala Likopano ka Li-Axes tsa Coordinate
Potso:
Fumana ntlha eo parabola e kopanang ho yona \( y^2 = -16x \) le di-coordinate axes.
Puisano:
Ho fumana ntlha eo ho kopanang ho yona le x-axis, re beha \( y = 0 \) ho equation ya parabola mme re fumana boleng ba \( x \).
\[ y^2 = -16x \]
Haeba \( y = 0 \):
\[ 0 = -16x \]
\[x = 0 \]
Kahoo, ntlha eo ho kopanang ho yona le x-axis ke \( (0, 0) \).
Ho fumana ntlha eo ho kopanang ho yona le mothapo wa y, re beha \( x = 0 \) mme re fumana boleng ba \( y \).
\[ y^2 = -16x \]
Haeba \( x = 0 \):
\[ y^2 = -16(0) \]
\[ y^2 = 0 \]
\[ y = 0 \]
Kahoo, ntlha ea ho kopana le mothapo oa y le eona ke \( (0, 0) \).
Kahoo, parabola \( y^2 = -16x \) e kopana feela le li-coordinate axes ntlheng \((0, 0) \).
Mohlala oa Potso ea 4: Ho taka Parabola
Potso:
Thala parabola ka equation \( y^2 = -4x \).
Puisano:
Ho taka parabola, re hloka ho tseba tlhahisoleseling ea bohlokoa:
– Parabola ena e shebane le letshehadi hobane coefficient ya x e mpe.
– Boleng ba \( 4a = -4 \) e le hore \( a = -1 \).
Ho tloha mona, re ka ngola:
– Sepheo sa parabola \( (-1, 0) \)
– Directrix \( x = 1 \)
Ha re taka, re ka hlalosa lintlha tse ling tse thusang:
– Haeba \( y = 2 \), \( x = -(\frac{4 \makgetlo a 2^2}{4}) = -1 \)
– Haeba \( y = -2 \), \( x = -(\frac{4 \times (-2)^2}{4}) = -1 \)
Ho sebedisa dintlha tse kang \((0, 0)\), \((-1, 2)\), le \((-1, -2)\) ho tla thusa ho taka parabola.
Qetello
Ho utloisisa likarolo tsa conic, haholo-holo parabola, ha ho bohlokoa feela thutong empa hape ho na le lits'ebetso tse ngata tse sebetsang. Ka mehlala ena ea mathata le lipuisano, babali ba lebelletsoe ho fumana kutloisiso e tebileng ea litšobotsi le tlhahlobo ea parabola. Ka ho tsoela pele ho ikoetlisa, kutloisiso ena e tla tebisa le ho nolofatsa tharollo ea mathata a kenyeletsang parabola.
