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Persamaan garis singgung lingkaran  dari titik  adalah ...

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Persamaan garis singgung lingkaran begin mathsize 14px style x squared plus y squared equals 36 end style dari titik begin mathsize 14px style open parentheses 9 comma negative 6 close parentheses end style adalah ...

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Pembahasan Soal:

 

begin mathsize 14px style x squared plus y squared equals 36 end style    

Titik begin mathsize 14px style open parentheses 9 comma negative 6 close parentheses end style disubtitusikan pada persamaan lingkaran

begin mathsize 14px style space space space space space x squared plus y squared equals 36 left right double arrow 9 squared plus left parenthesis negative 6 right parenthesis squared space left right double arrow 81 plus 36 left right double arrow 117 greater than 36 end style  

maka titik begin mathsize 14px style open parentheses 9 comma negative 6 close parentheses end style di luar lingkaran

Persamaan garis polar dari titik begin mathsize 14px style open parentheses 9 comma negative 6 close parentheses end style adalah

begin mathsize 14px style x x subscript 1 plus y y subscript 1 equals 36 9 x minus 6 y equals 36 9 x equals 6 y plus 36 x equals 2 over 3 y plus 4 end style 

 subtitusikan persamaan garis tersebut ke persamaan lingkaran

begin mathsize 14px style open parentheses 2 over 3 y plus 4 close parentheses squared plus y squared equals 36 4 over 9 y squared plus 16 over 3 y plus 16 plus plus y squared minus 36 equals 0 13 over 9 y squared plus 16 over 3 y minus 20 equals 0 13 y squared plus 48 minus 180 equals 0 open parentheses 13 y minus 30 close parentheses open parentheses y plus 6 close parentheses equals 0 y equals 30 over 13 space a t a u space y equals negative 6 y equals 30 over 13 rightwards arrow x equals 2 over 3 open parentheses 30 over 13 close parentheses plus 4 equals 72 over 13 y equals negative 6 rightwards arrow x equals 2 over 3 open parentheses negative 6 close parentheses plus 4 equals 0 end style 

Persamaan garis singgung yang melalui titik singgung begin mathsize 14px style open parentheses 72 over 13 comma 30 over 13 close parentheses end style dan begin mathsize 14px style open parentheses 0 comma negative 6 close parentheses end style adalah

begin mathsize 14px style left parenthesis 72 over 13 comma 30 over 13 right parenthesis rightwards arrow 72 over 13 x plus 30 over 13 y equals 36 space space space space space space space space space space space space space space space space space space space space 72 x plus 30 y equals 468 space space space space space space space space space space space space space space space space space space space space 12 x plus 5 y equals 78 left parenthesis 0 comma negative 6 right parenthesis rightwards arrow 0 times x minus 6 y equals 36 space space space space space space space space space space space space space space space space space space space space space space space space space space space y equals negative 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end style   

Jadi, persamaan garis singgung lingkaran  begin mathsize 14px style 12 x plus 5 y equals 78 end style dan begin mathsize 14px style y equals negative 6 end style 

 

 

 

 

 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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