Roboguru

Garis yang melalui titik O(0,0) dan P(a,b) berpoto...

Garis yang melalui titik O(0,0) dan P(a,b) berpotongan tegak lurus dengan garis singgung kurva y equals 9 over 2 minus x squared di P(a,b). Jika titik P berada di kuadran II, maka a + b adalah....

  1. negative 3 over 2

  2. negative 27 over 50

  3. fraction numerator 6 minus square root of 6 over denominator 2 end fraction

  4. fraction numerator 8 minus square root of 2 over denominator 2 end fraction

  5. fraction numerator 15 minus 2 square root of 3 over denominator 4 end fraction

Jawaban:

Ingat factorial space Garis space yang space melalui space dua space buah space titik space left parenthesis straight x subscript 1 comma straight y subscript 1 right parenthesis space dan space left parenthesis straight x subscript 2 comma straight y subscript 2 right parenthesis space memiliki  persamaan  fraction numerator straight y minus straight y subscript 1 over denominator straight y subscript 2 minus straight y subscript 1 end fraction equals fraction numerator straight x minus straight x subscript 1 over denominator straight x subscript 2 minus straight x subscript 1 end fraction  Garis space OP space melalui space titik space straight O left parenthesis 0 comma 0 right parenthesis space dan space straight P left parenthesis straight a comma straight b right parenthesis. space Maka space persamaan space garis space OP  adalah  fraction numerator straight y minus 0 over denominator straight b minus 0 end fraction equals fraction numerator straight x minus 0 over denominator straight a minus 0 end fraction  straight y over straight b equals straight x over straight a  box enclose straight y equals straight b over straight a straight x end enclose  Sehingga space gradien space garis space OP space adalah space box enclose straight m subscript 1 equals straight b over straight a end enclose    Karena space garis space singgung space kurva space berpotongan space tegak space lurus space dengan space garis space OP comma  maka space gradien space garis space singgung space kurva space left parenthesis yaitu space straight m subscript 2 right parenthesis space adalah  straight m subscript 1. straight m subscript 2 equals negative 1  straight b over straight a. straight m subscript 2 equals negative 1  box enclose straight m subscript 2 equals negative straight a over straight b end enclose    straight y equals 9 over 2 minus straight x squared  maka  straight m equals straight y apostrophe equals negative 2 straight x  Pada space titik space straight P left parenthesis straight a comma straight b right parenthesis comma space maka space gradien space garis space singgung space kurva space adalah  box enclose straight m subscript 2 equals negative 2 straight a end enclose    Didapatkan space box enclose straight m subscript 2 equals fraction numerator negative straight a over denominator straight b end fraction end enclose space dan space box enclose straight m subscript 2 equals negative 2 straight a end enclose comma space maka  minus straight a over straight b equals negative 2 straight a  1 over straight b equals 2  box enclose straight b equals 1 half end enclose    Karena space kurva space straight y equals 9 over 2 minus straight x squared space melalui space titik space straight P left parenthesis straight a comma straight b right parenthesis comma space maka  straight b equals 9 over 2 minus straight a squared  Karena space straight b equals 1 half comma space maka  1 half equals 9 over 2 minus straight a squared  straight a squared equals 4  straight a equals plus-or-minus 2  Karena space titik space straight P left parenthesis straight a comma straight b right parenthesis space berada space di space kuadran space II comma space maka space straight a less than 0 space dan space straight b greater than 0.  Sehingga space dipilih space box enclose straight a equals negative 2 end enclose.    Sehingga space straight a plus straight b equals negative 2 plus 1 half equals box enclose negative 3 over 2 end enclose

0

Ruangguru

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

Ikuti Kami

©2021 Ruangguru. All Rights Reserved