Geometría III Parabola

 

[`evkrsedhd Hfekrth ^hrh Hductis

Hsea`hturh: Akimktríh EEE-KDM 6>5

Tkmh:  Ch phrèfich Lhgecethdir:  Jiså Ck÷` Vkyks ^hrtegeph`tk:  Jucei Gkshr Vidreaukz

Mht. 6>82->6>, Wh`tehai dk cis Ghfhcckris, Vkpúfcegh Dime`egh`h

 

E`triduggei`

Chs phrèfic phrèfichs hs hphrkgk hphrkgk` ` k` del delkrk` krk`tks tks setuhge setuhgei`ks i`ks dk ch vedh vedh gitede gitedeh`h. h`h. Wk pukdk pukdk hprkgehr gchrhmk`tk guh`di ch`zhmis u` fhc÷` fimfkhdi i aicpkhmis u`h pkcith dk tk`es. K` ch gurvh quk dksgrefk ch pkcith k` su mivemek`ti sk pukdk vkr quk sk trhth dk u`h trhykgtireh phrhf÷cegh. Hc defujhr kstk dkspchzhmek`ti, pidkmis gi`sedkrhr ksth  phrèfich gimi ch rkprksk`thge÷` arèlegh dk u`h lu`ge÷` quk hsea`h h ghdh dkspchzhmek`ti birezi`thc nx' ch hcturh ny' hcgh`zhdh pir ch pkcith. [`h vkz se [`h setu tuhdh hdh ch phrèf phrèfic ich h k` ks kstk tk mhrg mhrgi, i, quk quk ks u` se sest stkm kmh h dk giird giirdk`h k`hdh dhs s ghrtkseh`hs, si` vesefcks dis pripekdhdks lu`dhmk`thcks: tek`k u` pu`ti kxtrkmi, quk girrkspi`dk hc e`sth`tk k` kc quk ch pkcith hcgh`zh ch hcturh mèxemh. Kstk pu`ti ks kc  vårtegk vårteg k dk ch phrèfich? y ch skau`dh, k` ch quk chs hcturhs h chs quk cckah ch pkcith si` chs mesmhs k` pisegei`ks birezi`thcks kquedesth`tks dk ch hfsgesh dkc vårtegk. ^ir th`ti, ch rkgth phrhckch hc kjk dk irdk`hdhs quk phsh pir kc vårtegk ks kc kjk dk semktríh dk ch  phrèfich.

 

 HGTE\E  DHD EEE. ^hrèfi ch

8. Bhcchr ch kguhge÷` dk ch phrèfich y gi`struer ch gurvh k` ghdh ghsi.  h) \ (6, 7), L (;, 7) 6

( y ∖ o ) =4 p ( x ∖b ) 6

( y ∖ 7) = 4.7 ( x ∖6 ) 6

( y ∖ 7) = 86 ( x ∖6)

 

 

f) \ (7, 8), Derkgtrez y = 7, L (7,-8), ^=-6  6

( x ∖b ) =∖4 p ( y ∖o ) 6

(  x ∖7 ) =4∑∖6 ( x ∖ 8) 6

( x ∖7 ) =∖2 ( y ∖8 ) 

 

 g) \ (-4, -7), Derkgtrez x =   6

( y ∖ o ) =∖4 p ( x ∖o ) 6

(  x ∖7 ) =4∑8> ( x + 4 ) 6

( x ∖7 ) =∖4> ( y + 4 ) 

 

d) \ (4, -6), chdi rkgti = 2, derkgge÷` IR― ^=6 L (>,4) Derkgtrez Derkgtrez y = -4 6

( x ∖b ) = 4  p ( y ∖o ) 6

(  x ∖ 4 ) = 2 ( x + 6) 6

( x ∖ 4 ) =2 ( y + 6) 

 

k) ch hfsgesh dkc ligi ks \ (8, -8) y kc kjk dk semktríh ks phrhckci h R9  L (>,>.;) Derkgtrez y=>.;  y

6

=6  px 6

(∖8 ) =6 p (8) =6  p

8

 p=

8 6

 p= >.; 6

( x ∖b ) = 4  p ( y ∖o ) 6

(  x ∖8 ) =6 ( x + 8 ) 6

( x ∖8 ) =6 ( y + 8 ) 

 

GI@GC[WEI@  Tidh lu`ge÷` guhdrètegh l(x) = hx6 + fx + g , rkprksk`th u`h phrèfich thc quk:  

Wu lirmh dkpk`dk kxgcusevhmk`tk dkc giklegek`tk h dk x6.

 

Cis giklegek`tks f  y g   trhschdh` ch phrèfich h ezquekrdh, dkrkgbh, hrrefh i hfhji.

 

We h 0 > , chs rhmhs vh` bhgeh hrrefh y se h 3 > , bhgeh hfhji.

 

Guh`ti mès arh`dk skh kc vhcir hfsicuti dk h, mès gkrrhdh ks ch phrèfich.

 

Kxestk u` ú`egi pu`ti dk girtk gi` kc kjk U, quk ks kc (>, y) i (>, g).

 

 

Cis girtks gi` kc kjk R sk iftek`k` rksicvek`di ch kguhge÷` hx6 + fx + g=> ,  pudek`di igurrer quk ci girtk k` dis pu`tis, k` u`i i k` `e`au`i. Ch premkrh giirdk`hdh dkc vårtegk ks  Rv = -f/6h.