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Garis singgung pada parabola yang sejajar dengan garis adalah ...

Garis singgung pada parabola begin mathsize 14px style y equals x squared plus 6 1 half x plus 14 1 half end style yang sejajar dengan garis begin mathsize 14px style x minus 2 y plus 3 equals 0 end style adalah ...

Jawaban:

Diketahui:

begin mathsize 14px style y equals x squared plus 6 1 half x plus 14 1 half end style
begin mathsize 14px style x minus 2 y plus 3 equals 0 end style

Mencari gradien:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x – 2 y plus 3 end cell equals cell 0 rightwards arrow straight a equals 1 comma straight b equals – 2 comma straight c equals 3 end cell row straight m equals cell – straight a over straight b end cell row straight m equals cell – fraction numerator 1 over denominator negative 2 end fraction end cell row straight m equals cell 1 half end cell end table end style  

Karena garis sejajar, maka begin mathsize 14px style straight m subscript 1 equals straight m subscript 2 equals 1 half end style.

Mencari titik singgung:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared plus open parentheses 6 1 half close parentheses x plus 14 1 half end cell row cell y ’ end cell equals cell 2 x plus 13 over 2 end cell row cell y ’ end cell equals cell straight m subscript 2 end cell row cell 2 x plus 13 over 2 end cell equals cell 1 half end cell row cell 2 x end cell equals cell 1 half – 13 over 2 end cell row cell 2 x end cell equals cell – 12 over 2 end cell row cell 2 x end cell equals cell – 6 end cell row x equals cell – 3 end cell end table end style 

Substitusi begin mathsize 14px style x equals – 3 end style pada persamaan garis singgung kurva:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared plus open parentheses 6 1 half close parentheses x plus 14 1 half end cell row y equals cell open parentheses negative 3 close parentheses squared plus open parentheses 6 1 half close parentheses open parentheses negative 3 close parentheses plus 14 1 half end cell row y equals cell 9 plus 13 over 2 open parentheses negative 3 close parentheses plus 29 over 2 end cell row y equals cell 9 – open parentheses 39 over 2 close parentheses plus 29 over 2 blank end cell row y equals cell 9 – 10 over 2 blank end cell row y equals cell 9 – 5 end cell row y equals 4 end table end style 

Diperoleh titik singgung begin mathsize 14px style open parentheses negative 3 comma space 4 close parentheses end style.

Didapat persamaan garis singgung:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses – 3 , space 4 close parentheses end cell rightwards arrow cell open parentheses x subscript 1 comma space y subscript 1 close parentheses end cell row cell y – y subscript 1 end cell equals cell straight m subscript 2 open parentheses x – x subscript 1 close parentheses end cell row cell y – 4 end cell equals cell 1 half open parentheses x – open parentheses negative 3 close parentheses close parentheses end cell row cell y – 4 end cell equals cell 1 half open parentheses x plus 3 close parentheses end cell row cell 2 open parentheses y – 4 close parentheses end cell equals cell x plus 3 end cell row cell 2 y – 8 end cell equals cell x plus 3 end cell row cell 2 y – x – 8 – 3 end cell equals 0 row cell 2 y – x – 11 end cell equals 0 end table end style 

Jadi, persamaan garis singgungnya adalah begin mathsize 14px style 2 y minus x minus 11 equals 0 end style.

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