Pertanyaan

(SBMPTN 2014) Jika lingkaran x 2 + y 2 − 2 a x + b = 0 mempunyai jari-jari 2 dan menyinggung x − y = 0 , maka nilai a 2 + b adalah ….

(SBMPTN 2014)

Jika lingkaran $x^{2} + y^{2} - 2 a x + b = 0$ mempunyai jari-jari 2 dan menyinggung $x - y = 0$ , maka nilai $a^{2} + b$ adalah ….

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Habis dalam

Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$begin mathsize 12px style x squared plus y squared minus 2 a x plus b equals 0 space P u s a t space l i n g k a r a n space colon space open parentheses negative 1 half space A comma negative 1 half space B close parentheses equals left parenthesis a comma 0 right parenthesis space J a r i minus j a r i space equals space 2 comma space m a k a space colon space r equals square root of open parentheses negative 1 half space A close parentheses squared plus open parentheses negative 1 half space B close parentheses squared minus C end root 2 equals square root of a squared plus 0 squared minus b end root space left parenthesis k e d u a space r u a s space d i k u a d r a t k a n right parenthesis space 4 equals a squared minus b space horizontal ellipsis.. left parenthesis i right parenthesis space J a r i minus j a r i space equals j a r a k space p u s a t space l i n g k a r a n space k e space g a r i s space x minus y equals 0 r equals open vertical bar fraction numerator a.1 plus 0. left parenthesis negative 1 right parenthesis plus 0 over denominator square root of 1 squared plus 0 squared end root end fraction close vertical bar space 2 equals a over 1 space left right arrow a equals 2 space S u b s t i t u s i k a n space n i l a i space a equals 2 space k e space p e r s a m a a n space left parenthesis i right parenthesis comma d i p e r o l e h space colon space 4 equals 2 squared minus b space b equals 4 minus 4 space b equals 0 space J a d i comma space n i l a i space a squared plus b equals 2 squared plus 0 equals 4. end style$