Roboguru
SD

Sebuah elips dengan persamaan 9x2​+4y2​=1 digeser sejauh (−12​), dilanjutkan dirotasi oleh [P(−1, 2), R(90∘)]. Persamaan bayangan elips tersebut adalah .... (SIMAK UNDIP 2013)

Pertanyaan

Sebuah elips dengan persamaan begin mathsize 14px style x squared over 9 plus y squared over 4 equals 1 end style digeser sejauh begin mathsize 14px style open parentheses table row cell negative 1 end cell row 2 end table close parentheses end style, dilanjutkan dirotasi oleh begin mathsize 14px style open square brackets straight P open parentheses negative 1 comma space 2 close parentheses comma space straight R open parentheses 90 degree close parentheses close square brackets end style. Persamaan bayangan elips tersebut adalah ....

(SIMAK UNDIP 2013)

  1. begin mathsize 14px style open parentheses x minus 3 close parentheses squared over 9 plus open parentheses y minus 3 close parentheses squared over 4 equals 1 end style 

  2. begin mathsize 14px style open parentheses x minus 1 close parentheses squared over 4 plus open parentheses y minus 2 close parentheses squared over 9 equals 1 end style 

  3. undefined 

  4. begin mathsize 14px style open parentheses x plus 1 close parentheses squared over 4 plus open parentheses y minus 2 close parentheses squared over 9 equals 1 end style 

  5. begin mathsize 14px style open parentheses x plus 1 close parentheses squared over 9 plus open parentheses y minus 2 close parentheses squared over 4 equals 1 end style 

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Elips begin mathsize 14px style x squared over 9 plus y squared over 4 equals 1 end style digeser sejauh begin mathsize 14px style open parentheses table row cell negative 1 end cell row 2 end table close parentheses end style maka, 

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared over 9 plus y squared over 4 end cell equals 1 row cell fraction numerator 4 x squared plus 9 y squared over denominator 9 cross times 4 end fraction end cell equals 1 row cell fraction numerator 4 x squared plus 9 y squared over denominator 36 end fraction end cell equals 1 row cell 4 x squared plus 9 y squared end cell equals 36 row cell open parentheses table row cell a apostrophe end cell row cell b apostrophe end cell end table close parentheses end cell equals cell open parentheses table row a row b end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell a minus 1 end cell row cell b plus 2 end cell end table close parentheses end cell row blank blank blank row cell a apostrophe end cell equals cell a minus 1 end cell row a equals cell a apostrophe plus 1 end cell row cell b apostrophe end cell equals cell b plus 2 end cell row b equals cell b apostrophe minus 2 end cell end table

Maka di dapat, a equals a apostrophe plus 1 dan b equals b apostrophe minus 2. Maka persamaan bayangan elipsnya yaitu 

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 a squared plus 9 b squared end cell equals 36 row cell 4 left parenthesis a apostrophe plus 1 right parenthesis squared plus 9 open parentheses b apostrophe minus 2 close parentheses squared end cell equals 36 row cell 4 left parenthesis x apostrophe plus 1 right parenthesis squared plus 9 open parentheses y apostrophe minus 2 close parentheses squared end cell equals 36 end table

Kemudian dilanjutkan denganrotasi oleh begin mathsize 14px style open square brackets straight P open parentheses negative 1 comma space 2 close parentheses comma space straight R open parentheses 90 degree close parentheses close square brackets end style

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 90 end cell cell negative sin space 90 end cell row cell sin space 90 end cell cell cos space 90 end cell end table close parentheses open parentheses table row cell x minus h end cell row cell y minus k end cell end table close parentheses plus open parentheses table row h row k end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses open parentheses table row cell x minus left parenthesis negative 1 right parenthesis end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses open parentheses table row cell x plus 1 end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell negative 1 left parenthesis y minus 2 right parenthesis end cell row cell 1 left parenthesis x plus 1 right parenthesis end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell negative y plus 2 end cell row cell x plus 1 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell negative y plus 1 end cell row cell x plus 3 end cell end table close parentheses end cell row cell x apostrophe end cell equals cell negative y plus 1 end cell row y equals cell negative x apostrophe plus 1 end cell row cell y apostrophe end cell equals cell x plus 3 end cell row x equals cell y apostrophe minus 3 end cell end table

Di dapat x equals y apostrophe minus 3 dan y equals negative x apostrophe plus 1 masukkan ke persamaan elips hasil translasi,

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 left parenthesis x apostrophe plus 1 right parenthesis squared plus 9 open parentheses y apostrophe minus 2 close parentheses squared end cell equals 36 row cell 4 left parenthesis y apostrophe minus 3 plus 1 right parenthesis squared plus 9 open parentheses x plus 3 minus 2 close parentheses squared end cell equals cell 36 space end cell row cell 4 open parentheses y minus 2 close parentheses squared plus 9 left parenthesis x plus 1 right parenthesis squared end cell equals cell 36 space end cell row cell open parentheses y minus 2 close parentheses squared over 9 plus fraction numerator left parenthesis x plus 1 right parenthesis blank squared over denominator 4 end fraction end cell equals 1 end table

Jadi, persamaan elipsnya adalahh table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses y minus 2 close parentheses squared over 9 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x plus 1 right parenthesis squared over 4 end cell 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 1 end table.


Oleh karena itu, jawaban yang benar adalah D.

126

0.0 (0 rating)

Pertanyaan serupa

SOAL UTBK REFERENSI 2021 Elips dengan persamaan 4x2+9y2=36 digeser (−12​)  kemudian diputar 90∘ dengan pusat (−1, 2). Persamaan bayangan elips tersebut adalah ....

58

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 Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

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