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Ïðèêëàä 4.2.14. Çíàéòè òî÷êè ïåðåòèíó êîëà<br />
2 2<br />
x + y = 1<br />
(4.2.9)<br />
ç îñÿìè êîîðäèíàò<br />
4.8. Ñêëàñòè ð³âíÿííÿ ìíîæèíè òî÷îê ïëîùèíè, äîáóòîê<br />
â³äñòàíåé ÿêèõ â³ä òî÷îê 1 (1, 0) i 2 (–1, 0) äîð³âíþº 1.<br />
2<br />
³äïîâ³äü: ( x 2 y 2 ) 2( x 2 y<br />
2<br />
)<br />
+ = - .<br />
4.9. Ñêëàñòè ð³âíÿííÿ ìíîæèíè òî÷îê ïëîùèíè, ð³âíîâ³ääàëåíèõ<br />
â³ä òî÷îê À(1, 1) ³ Â(3, 3).<br />
³äïîâ³äü: õ + ó − 4=0.<br />
2 2<br />
4.10. Çíàéòè òî÷êè ïåðåòèíó êîëà x + y = 50 ³ ïðÿìî¿<br />
ó – õ =0. ³äïîâ³äü: Ì 0 (5, 5), Ì 1 (–5, –5).<br />
4.3. вÂÍßÍÍß Ë²Í²¯ ÏÅÐØÎÃÎ ÏÎÐßÄÊÓ<br />
Ðèñ. 4.14<br />
Ðîçâ’ÿçàííÿ. Ïîêëàâøè ó = 0 â ð³âíÿííÿ (4.2.9), îäåðæèìî<br />
õ 2 = 1. Çâ³äê³ëÿ õ 1,2 = ±1.<br />
Òàêèì ÷èíîì, òî÷êè ïåðåòèíó À ³  êîëà ç â³ññþ Ox<br />
çíàéäåíî. Âîíè ìàþòü òàê³ êîîðäèíàòè: À(–1, 0), Â(1, 0).<br />
Àíàëîã³÷íî çíàõîäèìî êîîðäèíàòè òî÷îê ïåðåòèíó C i D<br />
êîëà ç â³ññþ Oy: C(0, –1), D(0, 1).<br />
ÂÏÐÀÂÈ<br />
4.6. Îäèí ê³íåöü â³äð³çêà çì³ùóºòüñÿ ïî îñ³ Îx, à äðóãèé<br />
— ïî îñ³ Îy. Çàïèñàòè ð³âíÿííÿ, ÿêå îïèñóº ïåðåì³ùåííÿ<br />
ñåðåäèíè öüîãî â³äð³çêà, ÿêùî äîâæèíà éîãî äîð³âíþº 2.<br />
2 2<br />
³äïîâ³äü: x + y = 1 .<br />
4.7. Ñêëàñòè ð³âíÿííÿ ë³í³¿, êîæíà òî÷êà ÿêî¿ çíàõîäèòüñÿ<br />
íà îäíàêîâ³é â³äñòàí³ â³ä òî÷êè<br />
³äïîâ³äü: y = x 2 .<br />
F æ 1ö ç 0, çè 4 ø÷<br />
³ ïðÿìî¿<br />
1<br />
y =- .<br />
4<br />
4.3.1. гâíÿííÿ ïðÿìî¿ ç êóòîâèì êîåô³ö³ºíòîì<br />
Ñïî÷àòêó ðîçãëÿíåìî ïðÿìó Ï 1 , ÿêà ïåðåòèíຠï³ä êóòîì<br />
α (0≤α
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