Pre-Calculus Quarter 1 - Module 3: Parabolas

 

99  

\rb-@ia`uaus  ‐ 

Yuirtbr 9  Fhmuab 04 \irijhais  \irijhais  

 

 

Uoit G Kbbm th Nkhw

 ]ogs fhmuab wis m mbsgekb bsgekbm m ikm wrgttbk wgto yhu gk fgkm. Gt gs obrb th o obap bap yhu fistbr tob mgccbrbkt @hkg` Pb`tghks. ]ob s`hpb hc togs fhmuab pbrfgts gt th jb usbm gk fiky mgccbrbkt abirkgke sgtuitghks. ]ob aikeuieb usbm rb`hekgzbs tob mgvbrsb vh`ijuairy abvba hc stumbkts. ]ob absshks irb irrikebm th chaahw tob stikmirm sbqubk`b hc tob `hursb. Jut tob hrmbr gk wog`o yhu rbim tobf `ik jb `oikebm th `hrrbsphkm wgto tob tbxtjhhn yhu irb khw usgke.  ]ob fhmuab gs mgvgmb mgvgmbm m gkth twh abss absshks, hks, kifbay kifbay44 • • •

  Absshk 0 ‐  0 ‐  \irijhais  \irijhais   Absshk = ‐  = ‐  Baagpsbs  Baagpsbs   Absshk 2 ‐  2 ‐  Oypbrjhais  Oypbrjhais

Ictbr ehgke torhueo togs fhmuab, yhu irb bxpb`tbm th4 9.  mbcgkb i pirijhai> :.  eripo i pirijhai egvbk ik bquitghk gk vbrtbx chrf> 0.  mbcgkb ik baagpsb> =.  eripo ik baagpsb egvbk ik bquitghk gk stikmirm chrf> 2.  mbcgkb i oypbrjhai> 3.  eripo i oypbrjhai egvbk ik bquitghk gk stikmirm chrf> 5.  rb`hekgzb tob bquitghk ikm gfphrtikt `oiri`tbrgstg`s hc tob mgccbrbkt typbs hc `hkg` sb`tghks> ikm ?.  shavbs sgtuitghkia prhjabfs gkvhavgke `hkg` sb`tghks.

:

 

 

Absshk 0

@hkg` Pb`tghks4 \irijhais

Ikhtobr typb hc `hkg`s gs i pirijhai. Whu oivb iarbimy abirkbm ijhut pirijhais jbchrb. Ikm wb wgaa curtobr mgs`uss gt gk togs absshk. Gk togs absshk, yhu wgaa abirk ohw th cgkm tob bquitghk hc i pirijhai gk vbrtbx chrf egvbk mgccbrbkt `hkmgtghks ikm ohw th eripo i pirijhai egvbk ik bquitghk gk vbrtbx chrf.

Uoit‗s Gk  

Whu stumgbm quimritg` cuk`tghks hc tob chrf y 6 ix : +jx + ` gk dukghr ogeo s`ohha ikm chukm hut toit jy `hfpabtgke tob squirb, yhu `ik rbwrgtb tob bquitghk gk tob vbrtbx chrf 6 i(x√ ℋ): + n.  ]ogs fhmuab w wgaa gaa oba obap p yhu gmbktgcy gmbktgcy shfb gf gfphrtikt phrtikt pirts pirts hc tob eripo hc i pirijhai agnb tob vbrtbx, agkb hc syffbtry, aitus rb`tuf, mgrb`trgx, ch`us usgke tob vbrtbx chrf. Whu wgaa iash abirk ohw th eripo pirijhai wgto bisb. Ph ehhm au`n, stiy ch`us ikm bkdhy tob mgccbrbkt i`tgvgtgbs toit wbrb prbpirbm  dust chr yhu!

0

 

 

=

 

 

Uoit gs Gt

Zbim tob chaahwgke `hk`bpts chr yhu th eigk jbttbr ukmbrstikmgke ijhut pirijhais. \IZIJHAIP Uoit gs i pirijhai8 

I  pirijhai   gs gs tob sbt hc iaa phgkts gk tob paikb bqugmgstikt crhf i cgxbm phgkt C ikm i cgxbm agkb a kht `hktigkgke C. Zbcbr th tob cgeurb jbahw.

 ]ob phgkt C gk tob mbcgkgtghk mbcgkgtghk ijhvb gs `iaabm tob  ch`us  hc   hc tob pirijhai ikm tob agkb A gs gts mgrb`trgx. mgrb`trgx. Gk  Gk togs absshk agkb a gs bgtobr ohrgzhktia hr vbrtg`ia. \irts hc tob \irijhai

@hksgmbr tob pirijhai wgto ch`us C ikm mgrb`trgx a.

2

 

 

 ]ob agkb torhueo torhueo C pbrpbkmg pbrpbkmg`uair `uair th a gs `iaabm tob ixgs hc syffbtry , hr sgfpay ixgs, hc tob pirijhai. ]ob ixgs hc syffbtry mgvgmbs tob pirijhai gkth twh pirts ikm tobsb pirts irb fgrrhr gfiebs. ]obrb gs bxi`tay hkb phgkt hc tob pirijhai toit agbs hk tob ixgs hc syffbtry. Gt gs `iaabm tob vbrtbx   hc tob pirijhai. Ub `ik sbb crhf tob mbcgkgtghk hc tob pirijhai toit tob vbrtbx gs bqugmgstikt crhf tob ch`us C ikm tob mgrb`trgx A. ]ob mgstik`b crhf tob vbrtbx th tob ch`us (hr mgrb`trgx) gs `iaabm tob ch`ia tob  ch`ia mgstik`b  mgstik`b   (i)  (i) . ]ob aitus rb`tuf  gs  gs i sbefbkt `hktigkgke tob ch`us, wgto bkmphgkts hk tob pirijhai ikm pbrpbkmg`uair th tob ixgs hc syffbtry. ]ob abketo hc tob aitus rb`tuf gs =i. Rsgke tob mgstik`b chrfuai chrfuai th chrf tob bquitghk hc tob pirijhai4

 ]ob stikmirm chrf hc ik b bquitghk quitghk hc i pi pirijhai rijhai wgto vbrtbx (