Roboguru

Pertanyaan

Lingkaran yang berpusat di (a,b) dengan begin mathsize 14px style straight a comma straight b greater than 3 end style, menyinggung garis begin mathsize 14px style 3 x plus 4 y equals 12 end style. Jika lingkaran tersebut berjari-jari 12, maka Error converting from MathML to accessible text.

D. Enty

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui:

Lingkaran berpusat di (a,b) dengan begin mathsize 14px style straight a comma straight b greater than 3 end style

Menyinggung garis begin mathsize 14px style 3 x plus 4 y equals 12 end style

Jari-jari lingkaran = 12

Ditanya: 

Error converting from MathML to accessible text.

Jawab:

Apabila diketahui persamaan garis begin mathsize 14px style ax plus by plus straight c equals 0 end style dan titik begin mathsize 14px style straight P open parentheses straight x subscript 1 comma end subscript straight y subscript 1 close parentheses end style,  maka jarak antara garis dengan titik dirumuskan Error converting from MathML to accessible text. .

Dari soal diketahui bahwa lingkaran berpusat di (a, b) dan menyinggung garis begin mathsize 14px style 3 x plus 4 y equals 12 end style, maka jarak antara titik usat ke garis singgung tersebut merupakan jari-jari lingkaran. Sehingga diperoleh persamaan berikut:

begin mathsize 14px style straight d equals straight r equals 12 end style

begin mathsize 14px style straight P left parenthesis straight x subscript 1 comma end subscript straight y subscript 1 right parenthesis equals straight P left parenthesis straight a comma straight b right parenthesis end style

begin mathsize 14px style 3 straight x plus 4 straight y equals 12 comma space maka straight a equals 3 comma space straight b equals 4 comma space dan space straight c equals negative 12 end style

space space space space space space space straight d space space equals vertical line fraction numerator ax subscript 1 plus by subscript 1 plus straight c over denominator square root of straight a squared plus straight b squared end root end fraction vertical line space space space space space space space space r space space equals vertical line fraction numerator 3 straight a plus 4 straight b minus 12 over denominator square root of 3 squared plus 4 squared end root end fraction vertical line space space space space space space space space r space space equals vertical line fraction numerator 3 straight a plus 4 straight b minus 12 over denominator square root of 9 plus 16 end root end fraction vertical line space space space space space space space space 12 equals vertical line fraction numerator 3 straight a plus 4 straight b minus 12 over denominator square root of 25 end fraction vertical line space space space space space space space space 12 equals vertical line fraction numerator 3 straight a plus 4 straight b minus 12 over denominator 5 end fraction vertical line space space space 12 cross times 5 equals 3 straight a plus 4 straight b minus 12 space space space space space space space space 60 equals 3 straight a plus 4 straight b minus 12 3 straight a plus 4 straight b equals 72

144

0.0 (0 rating)

Pertanyaan serupa

carilah persamaan garis singgung dari (x−2)2+(y+3)2=17 di titik (3,11)

7

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