8/12/2019 Parabola Theory E

1/16

EKPBW

"ekmdsbnuekrpbysdgs.dm" ;

Vkrklahk

Pbds gbkptjr cagussjs am pkrklahdg gurvjs, wbdgb gamstdtutjs amj gktjiary ac vkrdaus gurvjs altkdmj`

ly shdgdmi k gamj ly k phkmj, gkhhj` gamdg sjgtdams. K gamj (mat mjgjsskrdhy rdibt gdrguhkr) gkm lj aut

dm vkrdaus wkys ly k phkmj, km` tbus `dccjrjmt typjs ac gamdg sjgtdams krj altkdmj`.

Hjt us stkrt wdtb tbj `jcdmdtdam ac k gamdg sjgtdam km` tbjm wj wdhh sjj baw krj tbjy altkdmj` ly shdgdmik rdibt gdrguhkr gamj.

Gamdg Wjgtdams?K gamdg sjgt dam, ar gamdg ds tbj hagus ac k padmt wbdgb eavjs dm k phkmj sa tbkt dts `dstkmgj crae k c dxj`

padmt ds dm k gamstkmt rktda ta dts pjrpjm`dguhkr `dstkmgj crae k cdxj` strkdibt hdmj.

Pbj c dx j` padmt ds g khh j` tbjCagus.

Pbj cdxj` strkdibt h dmj ds gkhhj` tbj@drjgtrdx.

Pbj gamstkmt rktda ds gkhhj` tbjJggjmtrdgdty`jmatj` ly j.

jVE

VW

Pbj hdmj pkssdmi tbrauib tbj cagus & pjrpjm`dguhkr ta tbj drjgtrdx ds gkhhj` tbjKxds.

K padmt ac dmtjrsjgtdam ac k gamdg wdtb dts kxds ds gkhhj` k Sjrtjx.

Dc W ds (p, q) & `drjgtrdx ds x + ey + m 5 6

tbjm VW 5

8/12/2019 Parabola Theory E

2/16

EKPBW

"ekmdsbnuekrpbysdgs.dm" j = ;> 6> j = ;> 6

b 5 kl b 8 kl b = kl b = kl> k + l 5 6

VK\KLAHK@jc dm dt dam km` tjredmahaiy

K pkrklahk ds tbj hagus ac k padmt, wbasj `dstkmg j

crae k cdxj` padmt (cagus) ds jqukh ta pjrpjm`dguhkr

`dstkmgj crae k cdxj` strkdibt hdmj (`drjgtrdx).

Caur stkm`kr` cares ac tbj pkrklahk krj

y 5 0kx> y 5 0kx> x 5 0ky> x 5 0kyCar pkrklahk y< 5 0kx?

(d) Sjrtjx ds (6, 6) (dd) cagus ds (k, 6)

(ddd) Kxds ds y 5 6 (dv) @drjgtrdx ds x + k 5 6

Cagkh @dstkmgj?Pbj `dstkmgj ac k padmt am tbj pkrklahk crae tbj cagus.

Cagkh Gbar` ? K gbar` ac tbj pkrklahk, wbdgb pkssjs tbrauib tbj cagus.@aulhj Ar`dmktj?K gbar` ac tbj pkrklahk pjrpjm`dguhkr ta tbj kxds ac tbj syeejtry.

Hktus \jgtue? K `aulhj ar`dmktj pkssdmi tbrauib tbj cagus ar k cagkh gbar` pjrpjm`dguhkr ta tbj kxds

ac pkrklahk ds gkhhj` tbj Hktus \jgtue (H.\.).

Car y 5 0kx. Hjmitb ac tbj hktus rjgtue 5 0k. jm`s ac tbj hktus rjgtue krj H(k,

8/12/2019 Parabola Theory E

4/16

EKPBW

"ekmdsbnuekrpbysdgs.dm" 0

Jxkephj # ;? Cd m` tbj jquktd am ac tbj pkrklah k w bas j cag us d s kt ( ;,

8/12/2019 Parabola Theory E

5/16

EKPBW

"ekmdsbnuekrpbysdgs.dm" :

Wjhc Vrkgtdgj Vralhjes

(;) Cdm` tbj jquktdam ac tbj pkrklahk wbasj cagus ds tbj padmt (6, 6)km` wbasj `drjgtrdx ds tbj

strkdibt hdmj 7x 0y + < 5 6.

(

8/12/2019 Parabola Theory E

6/16

EKPBW

"ekmdsbnuekrpbysdgs.dm" 3

W;8 6Dmsd`j

W;= 6 Autsd`j

Jxkephj # 0 ? Gbjgn wbjtbjr tbj padmt (7, 0) hdjs dmsd`j ar autsd`j tbj pkklahk y< 5 0x.

Wahutdam ? y< 0x 5 6

W; y

;< 0x

;5 ;3 ;< 5 0 = 6

(7, 0) hdjs autsd`j tbj pkrklahk.

Wjhc Vrkgtdgj Vralhjes

(9) Cdm` tbj sjt ac vkhuj's ac car wbdgb (, < ) hdjs dmsd`j tbj pkrklahk y< + 0x 5 6.

Kmswjr ? ( 0 < 7 , 0 + < 7 )

Hdmj k pkrklahk ?Pbj hdmj y 5 ex + g ejjts tbj pkrklahk y 5 0kx dm twa padmts rjkh, gadmgd`jmt ar dekidmkry kggar`dmi

ks k

ge gam`dtdam ac tkmijmgy ds, g 5 k/e.Hjmitb ac tbj gbar` dmtjrgjptj` ly tbj pkrklahk

am tbj hdmj y 5 e x + g ds ?

Pkmijmt

Wjgkmt

K

L

8/12/2019 Parabola Theory E

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EKPBW

"ekmdsbnuekrpbysdgs.dm" 9

VW 5 k (; + t

8/12/2019 Parabola Theory E

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EKPBW

"ekmdsbnuekrpbysdgs.dm" 2

(dd) y 5 ex + k

e(e 6) kt

k

e

k

e