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Pertanyaan

Diketahuipersamaan hiperbola y 2 − 2 x 2 = 32 . Titik-titik fokusnya adalah ....

Diketahui persamaan hiperbola . Titik-titik fokusnya adalah ....

  1. begin mathsize 14px style left parenthesis 0 comma square root of 3 right parenthesis space dan space left parenthesis 0 comma negative square root of 3 right parenthesis end style

  2. begin mathsize 14px style left parenthesis 0 comma 2 square root of 3 right parenthesis space dan space left parenthesis 0 comma negative 2 square root of 3 right parenthesis end style

  3. begin mathsize 14px style left parenthesis 0 comma 3 square root of 3 right parenthesis space dan space left parenthesis 0 comma negative 3 square root of 3 right parenthesis end style

  4. begin mathsize 14px style left parenthesis 0 comma 4 square root of 3 right parenthesis space dan space space left parenthesis 0 comma negative 4 square root of 3 right parenthesis end style

  5. begin mathsize 14px style left parenthesis 0 comma 5 square root of 3 right parenthesis space dan space space left parenthesis 0 comma negative 5 square root of 3 right parenthesis end style

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Dari persamaan (i) diperoleh Sehingga diperoleh Jadi diperoleh titik fokusnya adalah

begin mathsize 14px style straight y squared minus 2 straight x squared equals 32 straight space ⟺ straight y squared over 32 minus fraction numerator 2 straight x squared over denominator 32 end fraction equals 1 ⟺ straight y squared over 32 minus straight x squared over 16 equals 1 space space.... space left parenthesis straight i right parenthesis end style

Dari persamaan (i) diperoleh
begin mathsize 14px style straight a squared equals 32 comma straight space straight a equals 4 square root of 2 straight b hat 2 equals 16 comma straight b equals 4 space end style

Sehingga diperoleh
begin mathsize 14px style space straight c squared equals straight a squared plus straight b squared space ⟺ straight c squared equals 32 plus 16 space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 48 space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight c equals square root of 48 equals 4 square root of 3 space end style 

Jadi diperoleh titik fokusnya adalah begin mathsize 14px style open parentheses 0 comma straight c close parentheses equals left parenthesis 0 comma 4 square root of 3 right parenthesis space dan space left parenthesis 0 comma negative straight c right parenthesis equals left parenthesis 0 comma negative 4 square root of 3 right parenthesis space end style

 

 

 

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Persamaan garis singgung dari persamaan hiperbola 8 x 2 ​ − 6 y 2 ​ = 1 di titik (2,3) (2, 3) adalah ....

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