Roboguru

Pertanyaan

Garis singgung dari kurva y equals fraction numerator x over denominator 2 minus 2 x end fraction yang melalui titik (1,-1) adalah ......

  1. x minus 8 y minus 9 equals 0

  2. x plus 4 y plus 3 equals 0

  3. 2 x minus 8 y minus 10 equals 0

  4. x plus 8 y plus 7 equals 0

  5. x minus 4 y minus 5 equals 0

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

straight y equals fraction numerator straight x over denominator 2 minus 2 straight x end fraction  Misalkan space titik space singgung space kurva space adalah space left parenthesis straight a comma straight b right parenthesis space maka space kurva space melalui space titik  left parenthesis straight a comma straight b right parenthesis comma space sehingga  box enclose straight b equals fraction numerator straight a over denominator 2 minus 2 straight a end fraction end enclose.... left parenthesis 1 right parenthesis    Untuk space mencari space gradien space dari space garis space singgung space pertama minus tama  harus space dicari space terlebih space dulu space turunan space pertama space dari space kurva space straight y equals fraction numerator straight x over denominator 2 minus 2 straight x end fraction  straight u equals straight x rightwards double arrow straight u apostrophe equals 1  straight v equals 2 minus 2 straight x rightwards double arrow straight v apostrophe equals negative 2  straight y apostrophe equals fraction numerator straight u apostrophe straight v minus uv apostrophe over denominator straight v squared end fraction equals fraction numerator 1 left parenthesis 2 minus 2 straight x right parenthesis minus straight x left parenthesis negative 2 right parenthesis over denominator left parenthesis 2 minus 2 straight x right parenthesis squared end fraction equals fraction numerator 2 minus 2 straight x plus 2 straight x over denominator left parenthesis 2 minus 2 straight x right parenthesis squared end fraction equals fraction numerator 2 over denominator left parenthesis 2 minus 2 straight x right parenthesis squared end fraction  Karena space titik space singgung space kurva space adalah space left parenthesis straight a comma straight b right parenthesis space maka  box enclose straight m equals fraction numerator 2 over denominator left parenthesis 2 minus 2 straight a right parenthesis squared end fraction end enclose.... left parenthesis 2 right parenthesis    Karena space kurva space melalui space titik space open parentheses straight x subscript 1 comma straight y subscript 1 close parentheses equals open parentheses straight a comma straight b close parentheses space dan space open parentheses straight x subscript 2 comma straight y subscript 2 close parentheses equals left parenthesis 1 comma negative 1 right parenthesis comma space maka  straight m equals fraction numerator straight y subscript 2 minus straight y subscript 1 over denominator straight x subscript 2 minus straight x subscript 1 end fraction  box enclose straight m equals fraction numerator negative 1 minus straight b over denominator 1 minus straight a end fraction end enclose.... left parenthesis 3 right parenthesis    Subtitusikan space persamaan space left parenthesis 2 right parenthesis space ke space persamaan space left parenthesis 3 right parenthesis  fraction numerator negative 1 minus straight b over denominator 1 minus straight a end fraction equals fraction numerator 2 over denominator left parenthesis 2 minus 2 straight a right parenthesis squared end fraction  fraction numerator negative 1 minus straight b over denominator 1 minus straight a end fraction equals fraction numerator 2 over denominator left parenthesis 2 minus 2 straight a right parenthesis left parenthesis 2 minus 2 straight a right parenthesis end fraction  fraction numerator negative 1 minus straight b over denominator 1 minus straight a end fraction equals fraction numerator 1 over denominator left parenthesis 1 minus straight a right parenthesis left parenthesis 2 minus 2 straight a right parenthesis end fraction  minus 1 minus straight b equals fraction numerator 1 over denominator left parenthesis 2 minus 2 straight a right parenthesis end fraction  Substitusikan space persamaan space left parenthesis 1 right parenthesis comma space maka  minus 1 minus fraction numerator begin display style straight a end style over denominator begin display style 2 minus 2 straight a end style end fraction equals fraction numerator 1 over denominator left parenthesis 2 minus 2 straight a right parenthesis end fraction  Kalikan space left parenthesis 2 minus 2 straight a right parenthesis  minus left parenthesis 2 minus 2 straight a right parenthesis minus straight a equals 1  minus 2 plus 2 straight a minus straight a equals 1  box enclose straight a equals 3 end enclose    Untuk space straight a equals 3 space maka space straight b equals fraction numerator straight a over denominator 2 minus 2 straight a end fraction equals fraction numerator 3 over denominator 2 minus 2 left parenthesis 3 right parenthesis end fraction equals box enclose negative 3 over 4 end enclose  straight m equals fraction numerator 2 over denominator left parenthesis 2 minus 2 straight a right parenthesis squared end fraction equals fraction numerator 2 over denominator left parenthesis 2 minus 2 left parenthesis 3 right parenthesis right parenthesis squared end fraction equals 2 over 16 equals box enclose 1 over 8 end enclose  straight y plus 3 over 4 equals 1 over 8 left parenthesis straight x minus 3 right parenthesis  Kalikan space kedua space ruas space dengan space 8  8 straight y plus 6 equals straight x minus 3  box enclose straight x minus 8 straight y minus 9 equals 0 end enclose

 

31

0.0 (0 rating)

Pertanyaan serupa

Persamaan garis singgung kurva y=x2−4x+3 yang sejajar dengan garis y=2x+3 adalah ....

75

0.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

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