Jika garis y = 2 - x memotong lingkaran x2+y2+2x−6y+2s=0 di dua titik, maka ....

Pertanyaan

Jika garis = 2 - x memotong lingkaran begin mathsize 14px style straight x squared plus straight y squared plus 2 straight x minus 6 straight y plus 2 straight s equals 0 end style di dua titik, maka ....

  1. s < 5

  2. s > 5

  3. s = 5

  4. s < -5

  5. s > -5

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Pertama, kita subtitusikan persamaan garis ke persamaan lingkaran tersebut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x squared plus straight y squared plus 2 straight x minus 6 straight y plus 2 straight s end cell equals 0 row cell straight x squared plus left parenthesis 2 minus straight x right parenthesis squared plus 2 straight x minus 6 left parenthesis 2 minus straight x right parenthesis plus 2 straight s end cell equals 0 row cell straight x squared plus 4 minus 4 straight x plus straight x squared plus 2 straight x minus 12 plus 6 straight x plus 2 straight s end cell equals 0 row cell 2 straight x squared plus 4 straight x minus 8 plus 2 straight s end cell equals 0 end table end style 

Diketahui garis tersebut memotong lingkaran begin mathsize 14px style straight x squared plus straight y squared plus 2 straight x minus 6 straight y plus 2 straight s equals 0 end style di dua titik, artinya persamaan kuadrat begin mathsize 14px style 2 straight x squared plus 4 straight x minus 8 plus 2 straight s equals 0 end style memiliki nilai diskriminan > 0, sehingga kita dapatkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight D greater than 0 row cell straight b squared minus 4 ac end cell greater than 0 row cell 4 squared minus 4 times 2 times left parenthesis negative 8 plus 2 straight s right parenthesis end cell greater than 0 row cell 16 plus 64 minus 16 straight s end cell greater than 0 row cell negative 16 straight s end cell greater than cell negative 80 end cell row straight s less than 5 end table end style  

Jadi, jawaban yang tepat adalah A.

74

5.0 (1 rating)

Pertanyaan serupa

Kedudukan garis y=x−1 dan y=2x+2 terhadap lingkaran x2+y2−2x+4y−6=0 berturut-turut adalah ....

97

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia