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Tentukan PGSL dari  yang bergradien !

Pertanyaan

Tentukan PGSL dari open parentheses x plus 2 close parentheses squared plus open parentheses y minus 2 close parentheses squared equals 16 yang bergradien square root of 8!

Pembahasan Soal:

Persamaan garis singgung bergradien m pada lingkaran L yang berpusat di open parentheses a comma b close parentheses dan jari-jari r adalah

y minus b equals m open parentheses x minus a close parentheses plus-or-minus r square root of 1 plus m squared end root

Diketahui lingkaran dengan persamaan open parentheses x plus 2 close parentheses squared plus open parentheses y minus 2 close parentheses squared equals 16. Lingkaran tersebut berpusat di open parentheses negative 2 comma 2 close parentheses dan jari-jari r equals square root of 16 equals 4. Persamaan garis singgung yang bergradien square root of 8 pada lingkaran tersebut sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m open parentheses x minus a close parentheses plus-or-minus r square root of 1 plus m squared end root end cell row cell y minus 2 end cell equals cell square root of 8 open parentheses x minus open parentheses negative 2 close parentheses close parentheses plus-or-minus 4 square root of 1 plus open parentheses square root of 8 close parentheses squared end root end cell row cell y minus 2 end cell equals cell square root of 8 open parentheses x plus 2 close parentheses plus-or-minus 4 square root of 1 plus 8 end root end cell row cell y minus 2 end cell equals cell square root of 8 x plus 2 square root of 8 plus-or-minus 4 square root of 9 end cell row cell y minus 2 end cell equals cell square root of 8 x plus 2 square root of 8 plus-or-minus 4 times 3 end cell row cell y minus 2 end cell equals cell square root of 8 x plus 2 square root of 8 plus-or-minus 12 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus 2 end cell equals cell square root of 8 x plus 2 square root of 8 plus 12 end cell row y equals cell square root of 8 x plus 2 square root of 8 plus 12 plus 2 end cell row blank equals cell square root of 8 x plus 2 square root of 8 plus 14 end cell end table 

atau

 table attributes columnalign right center left columnspacing 0px end attributes row cell y minus 2 end cell equals cell square root of 8 x plus 2 square root of 8 minus 12 end cell row y equals cell square root of 8 x plus 2 square root of 8 minus 12 plus 2 end cell row blank equals cell square root of 8 x plus 2 square root of 8 minus 10 end cell end table


Dengan demikian, PGSL dari open parentheses x plus 2 close parentheses squared plus open parentheses y minus 2 close parentheses squared equals 16 yang bergradien square root of 8 yaitu y equals square root of 8 x plus 2 square root of 8 plus 14 atau y equals square root of 8 x plus 2 square root of 8 minus 10

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Mei 2021

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