Pertanyaan

(SPMB 2003) Jika lingkaran x 2 + y 2 − 4 x − 6 y + c = 0 yang berpusat di titik (2, 3) menyinggung garis y = 1 − x , maka nilai c = ….

(SPMB 2003)

Jika lingkaran $x^{2} + y^{2} - 4 x - 6 y + c = 0$ yang berpusat di titik (2, 3) menyinggung garis $y = 1 - x$ , maka nilai c = ….

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Habis dalam

Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$begin mathsize 12px style x squared plus y squared minus 4 x minus 6 y plus c equals 0 space P u s a t space colon space open parentheses negative 1 half space A comma negative 1 half space B close parentheses equals left parenthesis 2 comma 3 right parenthesis space r equals square root of open parentheses negative 1 half space A close parentheses squared plus open parentheses negative 1 half space B close parentheses squared minus C end root space r equals square root of left parenthesis 2 right parenthesis squared plus left parenthesis 3 right parenthesis squared minus c end root space r equals square root of 13 minus c end root space m e n y i n g g u n g space g a r i s space y equals 1 minus x space left right arrow x plus y minus 1 equals 0 space J a r i minus j a r i space equals space j a r a k space t i t i k space p u s a t space left parenthesis 2 comma space 3 right parenthesis space k e space g a r i s space x plus y minus 1 equals 0 space r equals open vertical bar fraction numerator 1.2 plus 1.3 plus left parenthesis negative 1 right parenthesis over denominator square root of 1 squared plus 1 squared end root end fraction close vertical bar K a r e n a space r equals square root of 13 minus c end root space comma space m a k a space colon space square root of 13 minus c end root space equals fraction numerator 4 over denominator square root of 2 end fraction left parenthesis k e d u a space r u a s space d i k u a d r a t k a n right parenthesis comma space m a k a space colon space 13 minus c equals 16 over 2 space 13 minus c equals 8 space 13 minus 8 equals c space c equals 5 space space J a d i comma space n i l a i space c space a d a l a h space 5. end style$