Pertanyaan

Salah satu persamaan garis singgung lingkaran yang ditarik dari titik (0, 0) pada lingkaran ( x − 3 ) 2 + ( y − 4 ) 2 = 5 adalah ....

Salah satu persamaan garis singgung lingkaran yang ditarik dari titik (0, 0) pada lingkaran $(x - 3)^{2} + (y - 4)^{2} = 5$ adalah ....

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$begin mathsize 14px style S u b s t i t u s i k a n space t i t i k space left parenthesis 0 comma 0 right parenthesis space k e p e r s a m a a n space l i n g k a r a n colon open parentheses x minus 3 close parentheses squared plus open parentheses y minus 4 close parentheses squared equals 5 open parentheses x minus 3 close parentheses open parentheses 0 minus 3 close parentheses plus open parentheses y minus 4 close parentheses open parentheses 0 minus 4 close parentheses equals 5 minus 3 x plus 9 minus 4 y plus 16 equals 5 4 y equals 20 minus 3 x y equals fraction numerator 20 minus 3 x over denominator 4 end fraction equals 5 minus 3 over 4 x S u b s t i t u s i k a n space n i l a i space y space k e p e r s a m a a n space l i n g k a r a n colon open parentheses x minus 3 close parentheses squared plus open parentheses y minus 4 close parentheses squared equals 5 open parentheses x minus 3 close parentheses squared plus open parentheses 5 minus 3 over 4 x minus 4 close parentheses squared equals 5 open parentheses x minus 3 close parentheses squared plus open parentheses 1 minus 3 over 4 x close parentheses squared equals 5 x squared minus 6 x plus 9 plus 9 over 16 x squared minus 3 over 2 x plus 1 equals 5 25 over 16 x squared minus 15 over 2 x plus 10 equals 5 25 x squared minus 120 x plus 160 equals 80 25 x squared minus 120 x plus 80 equals 0 5 x squared minus 24 x plus 16 equals 0 open parentheses 5 x minus 4 close parentheses open parentheses x minus 4 close parentheses equals 0 x subscript 1 equals 4 over 5 space a t a u space x subscript 2 equals 4 M a k a space n i l a i space y space n y a x subscript 1 equals 4 over 5 rightwards arrow y equals 5 minus 3 over 4 x equals 5 minus 3 over 4 open parentheses 4 over 5 close parentheses equals 22 over 5 x subscript 2 equals 4 rightwards arrow y equals 5 minus 3 over 4 x equals 5 minus 3 over 4 open parentheses 4 close parentheses equals 2 P e r s a m a a n space g a r i s space sin g g u n g space l i n g k a r a n open parentheses x minus a close parentheses squared plus open parentheses y minus b close parentheses squared equals r squared p a d a space t i t i k space left parenthesis x subscript 1 comma space end subscript y subscript 1 right parenthesis space a d a l a h colon open parentheses x minus a close parentheses open parentheses x subscript 1 minus a close parentheses plus open parentheses y minus b close parentheses open parentheses y subscript 1 minus b close parentheses equals r squared U n t u k space t i t i k space open parentheses 4 over 5 comma space 22 over 5 close parentheses comma p e r s a m a a n space g a r i s space sin g g u n g space l i n g k a r a n n y a colon open parentheses x minus 3 close parentheses open parentheses 4 over 5 minus 3 close parentheses plus open parentheses y minus 4 close parentheses open parentheses 22 over 5 minus 4 close parentheses equals 5 open parentheses x minus 3 close parentheses open parentheses negative 11 over 3 close parentheses plus open parentheses y minus 4 close parentheses open parentheses 2 over 5 close parentheses equals 5 minus 11 x plus 33 plus 2 y minus 8 equals 25 minus 11 x plus 2 y equals 0 11 x minus 2 y equals 0 U n t u k space t i t i k space open parentheses 4 comma 2 close parentheses comma p e r s a m a a n space g a r i s space sin g g u n g space l i n g k a r a n n y a colon open parentheses x minus 3 close parentheses open parentheses 4 minus 3 close parentheses plus open parentheses y minus 4 close parentheses open parentheses 2 minus 4 close parentheses equals 5 open parentheses x minus 3 close parentheses plus open parentheses y minus 4 close parentheses open parentheses negative 2 close parentheses equals 5 x minus 3 minus 2 y plus 8 equals 5 x minus 2 y equals 0 end style$