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Salah satu persamaan garis singgung lingkaran x 2 + y 2 − 10 x + 2 y + 1 = 0 yang tegak lurus dengan garis 5 x + 12 y − 8 = 0 adalah.......

Salah satu persamaan garis singgung lingkaran yang tegak lurus dengan garis adalah.......

  1. 5y - 12x - 130 = 0

  2. 5y - 12x + 130 = 0

  3. 5y + 12x + 130 = 0

  4. 5x - 12y + 130 = 0

  5. 5x + 12y + 130 = 0

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Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

P e r s a m a a n space g a r i s space 5 x plus 12 y minus 8 equals 0 space b e r g r a d i e n space m subscript 1 equals negative 5 over 12 comma space  m a k a space g r a d i e n space g a r i s space y a n g space t e g a k space l u r u s space g a r i s space t e r s e b u t space b e r l a k u space r u m u s space colon space space m subscript 1 m subscript 2 equals negative 1 left right double arrow m subscript 2 equals 12 over 5  P e r s a m a a n space g a r i s space sin g g u n g space p a d a space l i n g k a r a n space d e n g a n space p u s a t space left parenthesis a comma b right parenthesis space comma space b e r j a r i space – space j a r i space r space d a n space b e r g r a d i e n space m space a d a l a h  y minus b equals m open parentheses x minus a close parentheses plus-or-minus r square root of m squared plus 1 end root  P e r s a m a a n space l i n g k a r a n space x squared plus y squared plus A x plus B y plus C equals 0 space m e m i l i k i space p u s a t space P open parentheses negative 1 half A comma negative 1 half B close parentheses space d a n space j a r i minus j a r i space r equals square root of 1 fourth A squared plus 1 fourth B squared minus C end root    M a k a space p e r s a m a a n space g a r i s space sin g g u n g space l i n g k a r a n space x squared plus y squared minus 10 x plus 2 y plus 1 equals 0 space d e n g a n space space p u s a t space  P open parentheses negative 1 half open parentheses negative 10 close parentheses comma negative 1 half open parentheses 2 close parentheses close parentheses identical to P open parentheses 5 comma negative 1 close parentheses  d a n space j a r i space – space j a r i space colon space r equals square root of 1 fourth open parentheses negative 10 close parentheses squared plus 1 fourth open parentheses 2 close parentheses squared minus 1 end root equals 5  a d a l a h  y minus open parentheses negative 1 close parentheses equals 12 over 5 open parentheses x minus 5 close parentheses plus-or-minus 5 square root of open parentheses 12 over 5 close parentheses squared plus 1 end root  y plus 1 equals 12 over 5 open parentheses x minus 5 close parentheses plus-or-minus 5 open parentheses 13 over 5 close parentheses  K a l i k a n space k e d u a space r u a s space d e n g a n space 5  5 open parentheses y plus 1 close parentheses equals 12 open parentheses x minus 5 close parentheses plus-or-minus 5 open parentheses 13 close parentheses  5 y plus 5 equals 12 x minus 60 plus-or-minus 65  12 x minus 5 y minus 65 plus-or-minus 65 equals 0  A d a space d u a space p e r s a m a a n  12 x minus 6 y minus 65 plus 65 equals 0  12 x minus 5 y equals 0  A t a u  12 x minus 6 y minus 65 minus 65 equals 0  12 x minus 5 y minus 130 equals 0  5 y minus 12 x plus 130 equals 0

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Tentukan persamaan garis singgung lingkaran x 2 + y 2 − 4 y − 21 = 0 melalu titik A(1,-5)

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