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Tentukan nilai a agar lingkaran (x–2a)2+(y–3)2=5+a2  menyinggung sumbu-x.

Pertanyaan

Tentukan nilai begin mathsize 14px style a end style agar lingkaran begin mathsize 14px style left parenthesis x – 2 a right parenthesis squared plus left parenthesis y – 3 right parenthesis squared equals 5 plus a squared end style  menyinggung sumbu-begin mathsize 14px style x end style.

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

lingkaran begin mathsize 14px style left parenthesis x – 2 a right parenthesis squared plus left parenthesis y – 3 right parenthesis squared equals 5 plus a squared end style  akan menyinggung sumbu-begin mathsize 14px style x end style jika nilai begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style.

Pembahasan

Perhatikan gambar persamaan lingkaran begin mathsize 14px style left parenthesis x minus a right parenthesis squared plus left parenthesis y minus b right parenthesis squared equals r to the power of 2 end exponent end style yang menyinggung sumbu-begin mathsize 14px style x end style berikut:

Pada gambar jelas terlihat bahwa jari-jari lingkaran pusat begin mathsize 14px style left parenthesis a comma space b right parenthesis end style yang menyinggung sumbu-undefined memiliki begin mathsize 14px style r equals b end style, maka lingkaran begin mathsize 14px style left parenthesis x – 2 a right parenthesis squared plus left parenthesis y – 3 right parenthesis squared equals 5 plus a squared end style memiliki nilai begin mathsize 14px style r equals square root of 5 plus a squared end root end style dan begin mathsize 14px style b equals 3 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row r equals b row cell square root of 5 plus a squared end root end cell equals 3 row cell open parentheses square root of 5 plus a squared end root close parentheses squared end cell equals cell 3 squared end cell row cell 5 plus a squared end cell equals 9 row cell a squared plus 5 minus 9 end cell equals 0 row cell a squared minus 4 end cell equals 0 row cell left parenthesis a plus 2 right parenthesis left parenthesis a minus 2 right parenthesis end cell equals 0 row blank blank blank end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style

Jadi lingkaran begin mathsize 14px style left parenthesis x – 2 a right parenthesis squared plus left parenthesis y – 3 right parenthesis squared equals 5 plus a squared end style  akan menyinggung sumbu-begin mathsize 14px style x end style jika nilai begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style.

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