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Test nga lënda e Matematikës
2. Shqyrtoni pozitën reciproke ndërmjet drejtëzës dhe parabolës: .
4. Të gjenden rrezet vatrore të elipsës, në qoftë se është dhënë elipsa dhe vizato
5. Të konstruktohet grafiku i parabolës .
Emri dhe Mbiemri

Ask by Guzman Sullivan. in Serbia
Dec 09,2024

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Answer

  1. Shqyrtimi i pozitës reciproke ndërmjet drejtëzës dhe parabolës .
  2. Gjetja e rrezete vatrore të elipsës .
  3. Konstruktimi i grafikut të parabolës .
    Emri dhe Mbiemri: [Emri i autorit]

Solution

  1. Shqyrtimi i pozitës reciproke ndërmjet drejtëzës dhe parabolës:
    Për të shqyrtuar pozitën reciproke ndërmjet drejtëzës dhe parabolës, duhet të gjejmë të dy elementët matematikë që përshkruanë drejtëzën dhe parabolën.
Drejtëza e dhënë është , ndërsa parabola është .
  1. Gjetja e rrezete vatrore të elipsës:
    Elipsa e dhënë është . Rrezet vatrore të elipsës janë të dhëna nga formula e elipsës, ku rrezet vatrore janë dhe , ku është gjysma e diametrin e elipsës, ndërsa është shkalla e elipsës.
  2. Konstruktimi i grafikut të parabolës:
    Parabola e dhënë është . Për të vizatuar grafikun e parabolës, duhet të gjejmë të dy elementët matematikë që përshkruanë parabolën, të cilët janë shkalla e parabolës dhe pozita e qendrës së parabolës.
Emri dhe Mbiemri: [Emri i autorit]

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Për pozitat reciproke ndërmjet drejtëzës dhe parabolës, mund të zëvendësoni shprehjen e drejtëzës në ekuacionin e parabolës, duke e bërë . Kjo do të rezultojë në një ekuacion të rendit të dytë që mund të zgjidhet për të gjetur pikët e prerjes, duke caktuar kështu pozitat reciproke të dy formave grafike.
Për elipsën e dhënë , mund të rregullojmë ekuacionin në formën standard të elipsës, . Pas kësaj, ashtu si rrezet vatrore janë të vendosura në qendër të elipsës dhe mund të llogariten si , ku dhe janë gjatësitë e poligonëve në x dhe y. Rrezet e elipsës në këtë rast janë .

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