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DF\GY

"dfmesgoudfrpgyseis.em" 6

N``epsn

Em tges igfptnr wn frn caemc ta lesiuss em lntfe` tgn mfturn ah pftg em wgeig am p`fmnts davn frauml tgn sum.

\gny ha``aw am n``epteif` pftg wetg tgn sum ft amn ah ets haie. @nt us `aao ft tgn lnhemeteam ah n``epsn.

Lnhemeteams 2 -Et es `aius ah f paemt wgeig davns em suig f wfy tgft tgn rftea ah ets lestfmin hrad f hexnl paemt fml f

hexnl `emn (mat pfssns tgraucg hexnl paemt fml f`` paemts fml `emn `ens em sfdn p`fmn) es iamstfmt (n),

wgeig es `nss tgfm amn.

\gn hexnl paemt es if``nl - haius

\gn hexnl `emn es if``nl -lernitrex.

\gn iamstfmt rftea es if``nl - niinmtreiety, et es lnmatnl ky'n'.

Nxfdp`n # 6 2 Heml tgn nqufteam ta tgn n``epsn wgasn haius es tgn paemt ( 6, 6), wgasn lernitrex es tgn strfecgt

`emn x y + 9 4 : fml niinmtreiety es;6 .

Ya`uteam 2 @nt Z(g, o) kn davemc paemt,

n 4ZD

ZY4

;

6

(g + 6); + (o 6); 4 4 >9 .

@nmctg ah `ftus rnitud 4 @@ 4f

k; ;

4>

68; 4

>

9;

Ia-arlemftns haiee frn W 4 fn, U 4 :

Y (W 4 9, U 4 :) & Y (W 4 9, U 4 :) Y (8, ;) & Y (:, ;)

I a - a r l e m f t n a h v n r t e i n s

Nxtrndetens ah dfbar fxes F(W 4 f, U 4 :) & F (W 4 f, U 4 :) F (x 4 7, y 4 ;) & F 4 (x 4 ;, ;)

F (7, ;) & F ( ;, ;)Nxtrndetens ah demar fxes K (W 4 :, U 4 k) & K (W 4 :, U 4 k)

K (x 4 9, y 4 8) & K (x 4 9, y 4 ;)K (9, 8) & K (9, ;)

Nqufteam ah lernitrex W 4 n

f

x 9 4 9

;> x 4

9

9

(9) Heml tgn niinmtreiety ah n` epsn wgasn demar fxes es lauk`n tgn `ftus rnitud.

(7y 6>6 4 :.

(9);

9((>) 9x; +

8/12/2019 Ellipse Theory e

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DF\GY

"dfmesgoudfrpgyseis.em" 8

Nfdp`n # 7 2 Heml tgn lestfmin hrad inmtrn ah tgn paemt Z am tgn n``epsn ;

;

f

x+ ;

;

k

y4 6 wgasn rfleus dfons

fmc`n wetg x-fxes.Ya`uteam 2 @nt Z (f ias, k sem)

d(ap)

4f

ktfm 4 tfm tfm4

k

ftfm

AZ 4 ;;;; semkiasf 4

;

;;;

sni

tfmkf

4

;

;;;

tfm6

tfmkf4

;

;

;

;

;

;;;

tfmk

f6

tfmk

fkf

AZ4

;;;; iasksemf

fk

Yn`h Zrfitein Zrak`nd

(3) Heml tgn lestfmin hrad inmtrn ah tgn paemt Z am tgn n` epsn ;

;

f

x+ ;

;

k

y4 6 wgasn niinmtrei

fmc`n es

(7) Heml tgn niinmtrei fmc`n ah f paemt am tgn n` epsn8

x;+

;

y;4 6 wgasn lestfmin hrad tgn

inmtrn es ;.

(5) Ygaw tgft tgn frnf ah trefmc`n emsireknl em fm n` epsn knfrs f iamstfmt rftea ta tgn frnf ah tgn

trefmc`n hardnl ky baememc paemts am tgn fuxe`efry ieri`n iarrnspamlemc ta tgn vnrteins ah tgn herst

trefmc`n.

Fmswnrs 2 (3) ;;;; semkiasfr (7)

Nxfdp`n#;6 2 Zravn tgft, em fm n``epsn, tgn lestfmin kntwnnm tgn inmtrn fml fmy mardf` lans mat nxinnl tgn

lehhnrnmin kntwnnm tgn snde-fxns ah tgn n``epsn.

Ya`uteam 2 @nt tgn nqufteam ah n``epsn es 6k

y

f

x;

;

;

;

Nqufteam ah mardf` ft Z () es (f sni)x (kiasni)y f; + k; 4 :lestfmin ah mardf` hrad inmtrn

4 A[ 4;;;;

;;

)iatk()tfmf(kf

|kf|

4;;

;;

)iatktfmf()kf(

|kf|

(f + k); + (f tfm k iat); (f + k); ar ;

;;

)kf(|kf|

|A[|(f k)

Yn`h Zrfitein Zrak`nd

(;:) Heml tgn vf`un(s) ah 'o' har wgeig tgn emn x + y 4 o es f mardf` ta tgn n` epsn 6k

y

f

x;

;

;

;

(;6) Eh tgn mardf` ft tgn paemt Z() ta tgn n``epsn>

y

6

;,

;

6

Fmswnrs 2 (;8) x + ;y 4 < (;3)

;

;

;

;

;

k

y

f

x

;

8

;

8

y

k

x

f

4 (f

;

k

;

)

;

(;7)>

3

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DF\GY

"dfmesgoudfrpgyseis.em" 63

(;) \gn tfmcnmt & mardf` ft f paemt Z am tgn n` epsn kesnit tgn nxtnrmf` & emtnrmf` fmc`ns kntwnnm tgn haif`

lestfmins ah Z. \ges rnhnrs ta tgn wn`` omawm rnh`niteam prapnrty ah tgn n``epsn wgeig stftns tgft rfyshrad amn haius frn rnh`nitnl tgraucg atgnr haius & veinvnrsf. Gnmin wn ifm lnluin tgft tgn strfecgt`emns baememc nfig haius ta tgn haat ah tgn pnrpnmleiu`fr hrad tgn atgnr haius upam tgn tfmcnmt ft fmy

paemt Z dnnt am tgn mardf` ZC fml kesnits et wgnrn C es tgn paemt wgnrn mardf` ft Z dnnts tgn dfbar

fxes.

(9) \gn praluit ah tgn `nmctgs ah tgn pnrpnmleiu`fr sncdnmts hrad tgn haie

am fmy tfmcnmt ta tgn n``epsn es k fml tgn hnnt ah tgnsn pnrpnmleiu`frs

`en am ets fuxe`efry ieri`n fml tgn tfmcnmts ft tgnsn hnnt ta tgn fuxe`efry

ieri`n dnnt am tgn arlemftn ah Z fml tgft tgn `aius ah tgner paemt ah

emtnrsniteam es f sede`efr n``epsn fs tgft ah tgn arecemf` amn.

() Eh tgn mardf` ft fmy paemt Z am tgn n` epsn wetg inmtrn I dnnt tgn dfbar & demar fxns em C & c

rnspnitevn`y, & eh IH kn pnrpnmleiu`fr upam tges mardf` , tgnm

(e) ZH. ZC 4 k

(ee) ZH. Zc 4 f

( eee) ZC. Zc 4 YZ. YZ(ev) IC. I\ 4 IY;

(v) `aius ah tgn del paemt ah Cc es fmatgnr n``epsn gfvemc

tgn sfdn niinmtreiety fs tgft ah tgn arecemf` n``epsn.

_wgnrn Y fml Yfrn tgn haiee ah tgn n``epsn fml \ es tgn paemt wgnrn tfmcnmt ft Z dnnt tgn dfbar fxesT

(8) \gn ieri`n am fmy haif` lestfmin fs lefdntnr tauigns tgn fuxe efry ieri`n. Znrpnmleiu`frs hrad tgninmtrn upam f`` igarls wgeig baem tgn nmls ah fmy pnrpnmleiu`fr lefdntnrs ah tgn n``epsn frn ah iamstfmt

`nmctg.

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DF\GY

(3) Eh tgn tfmcnmt ft tgn paemt Z ah f stfmlfrl n` epsn dnnts tgn fxes em \ fml t fml IU es tgn pnrpnmleiu`fram et hrad tgn inmtrn tgnm,

(e) \ t. ZU 4 f; k ; fml (ee) `nfst vf` un ah \ t es f + k.