????????? [ ???????? | ???????? ???? ]

???????? ??????? ? ?????????? ??? ?????? ???????????? ????, ????? ?????????????????? ???????????? ??????? ????? ????? ${\displaystyle F_{1}}$ ? ${\displaystyle F_{2}}$ ??????? (????? ??????? ?? ????????? ????????? ??? ?????????) ????????? ??

${\displaystyle {\bigl |}|PF_{1}|-|PF_{2}|{\bigr |}=2a,}$ ??? ${\displaystyle |F_{1}F_{2}|>2a>0}$

${\displaystyle F_{1}F_{2}}$ ??????? ?????????????, ??? ?????????? ${\displaystyle 2c}$-??, ??????? ? ?????????? ??????????????, ??? ${\displaystyle F_{1}F_{2}}$-? ?????????? ????????? ???????? ?????????? ??? ??????????? ???????????? ????????? ??????? ??????, ?? ${\displaystyle Ox}$ ??????? ????? ${\displaystyle F_{1}}$ ? ${\displaystyle F_{2}}$ ???????, ??? ${\displaystyle Oy}$ ???????? ${\displaystyle F_{1}F_{2}}$-? ?????????? (????? ?????)? ??? ??????? ${\displaystyle F_{1}}$ ? ${\displaystyle F_{2}}$ ?????? ????????????? ???????????????? ?????? ${\displaystyle (-c,0)}$ ? ${\displaystyle (c,0)}$? ?????? ${\displaystyle M(x;y)}$-? ????????? ????????? ??? ?. ??? ???????? ??????????

${\displaystyle |PF_{1}-PF_{2}|=2a}$

???

${\displaystyle PF_{1}-PF_{2}=\pm 2a}$

???????? ????? ?????? ????????????? ????????? ??????? ????

${\displaystyle {\sqrt {(x+c)^{2}+y^{2}}}-{\sqrt {(x-c)^{2}+y^{2}}}=\pm 2a}$ (1)

?? ?? ???? ??????????? ? ????????? ??????????? ??????? ????????????? ???????????? ??????? ?????????? ?????? ?????????? ?? ??? ? ????? ????? ??????????? ?????????,

${\displaystyle (x+c)^{2}+y^{2}=4a^{2}\pm 4a{\sqrt {(x-c)^{2}+y^{2}}}+(x-c)^{2}+y^{2}}$

???? ?????????????????? ???? ??????? ??? `

${\displaystyle (c^{2}-a^{2})x^{2}-a^{2}y^{2}=a^{2}(c^{2}-a^{2})}$

???? ?? ( ??? ???????? ????????????????) ${\displaystyle c>a}$, ??? ${\displaystyle c^{2}-a^{2}>0}$: ?????????? ${\displaystyle b^{2}=c^{2}-a^{2}}$, ????????

${\displaystyle b^{2}x^{2}-a^{2}y^{2}=a^{2}b^{2}}$

???

${\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1}$, (2)

??? ??????? ? ????????? ????????? ??????????? ?????? ? ?????? ???????, ?????? ? ????? ???, ?? ???? ? ??? ??????? ??????? (2)-?? ????????? ???????? ${\displaystyle M(x;y)}$ ??? ?????????? ? ??? (1)-???

${\displaystyle Ox}$ ??????? ??????? ? ????????? ?????? ?????? ${\displaystyle Oy}$-?` ???? ??????? ${\displaystyle 2a}$-? ? ${\displaystyle 2b}$-? ??????? ?? ????????? ?????? ? ???? ?????????? ???????????????? ${\displaystyle w={\frac {c}{a}}}$ -? (?????? ${\displaystyle w=\varepsilon }$) ??????? ? ????????? ?????????????? ? ?????? ? ????????? ????? ${\displaystyle x=-{\frac {a}{w}}}$ (?????? ${\displaystyle w=\varepsilon }$) ? x = ${\displaystyle {\frac {a}{w}}}$ (?????? ${\displaystyle w=\varepsilon }$) ????????? ??????? ?? ??????????????

??????????? ???? ???????, ????? ?????????? ?? ≪????????≫ ?????????

?????????? ? ??????????????? ????????? (11-??) · ????????? · ?????????? ? ?????? · ??????? · ??????? · ??? ????????? (1 ???.) ???????????? ???????????????? GND :  4161034-9 · Microsoft :  145050668 · NKC :  ph973163

??? ??????? ??? ??? ????? ??????? ??????? ????????? ??? ???????? ????????? ??????? ? ???????? ??????? ?????????????? ???????? 3.0 (Creative Commons BY-SA 3.0) ???? ????????????? ????????? ???????? ????????? ??????????????   ( ?? 6, ?? 415 )?