Kurva-Kurva Baku

14 Juni 10

Ada 5 jenis setidaknya kurva yang termasuk kurva baku yaitu garis lurus, lingkaran, parabola, hiperbola dan elips.. yuk kita simak apa aja.. Check this out…

  1. Garis Lurus
    Yang pertama dibahas adalah kemiringan (slope) biasa kita sebut gradien,
    m=dy/dx={y_2-y_1}/{x_2-x_1}
    Sedangkan sudut antara dua garis
    tan theta={m_2-m_1}/{1+m_1m_2}
    Untuk dua garis sejajar,
    m_2=m_1
    Untuk dua garis yang saling tegak lurus,
    m_2 . m_1=-1
    Persamaan garis lurus dengan kemiringan = m

    1. Jika mematong sumbu y di titik (o,c), maka y = mx+c
    2. Jika melalui (x_1,y_1), maka y-y_1=m(x-x_1)
    3. Jika melalui (x_1,y_1) dan (x_2,y_2), maka {y-y_1}/{y_2-y_1}={x-x_1}/{x_2-x_1}
  2. Linkaran
    Berpusat di titik asal (0,0) , maka
    x^2+y^2=r^2
    Berpusat di (a,b) dengan jari-jari r, maka
    (x-a)^2+(y-b)^2=r^2
    Sedangkan persamaan umumnya adalah :
    x^2+y^2+2ax+2by+c=0
    Jika diketahui dengan pusat (-a,-b), maka
    r=sqrt{a^2+b^2-c}
  3. Parabola
    Jika verteks parabola di titik (0,0) dan fokusnya di (a,0) maka kurvanya adalah:
    y^2=4ax
    Sedangkan persamaan parametriknya adalah :
    x=at^2 dan y=2at
  4. Ellips
    Sebuah ellips dengan pusat (0,0) dan fokus di (pm sqrt{delim{[}{x^2-b^2}{]}},0)
    {x^2/a^2}+{y^2/b^2}=1
    dengan a setengah sumbu panjang dan b adalah setengah sumbu pendek.
    Sedangkan persamaan parametriknya adalah:
    x=a cos theta dan y=b sin theta
  5. Hiperbola
    Sebuah hiperbola dengan pusat (0,0) dan fokus di (pm sqrt{delim{[}{x^2+b^2}{]}},0)
    {x^2/a^2}-{y^2/b^2}=1
    Persamaan parametriknya:
    x=a sec theta dan y=b tan theta

    Sedangkan hiperbola tegak:
    Berpusat di (0,0), fokus pm({a/sqrt{2}},{a/sqrt{2}}) kurvanya xy=a^2/2=c^2
    dengan c=a/sqrt{2}
    Persamaan parametrik: x=ct dan y=c/t

Yup.. selamat belajar…
Sumber : Matematika Untuk Teknik (Kastroud, Erwin Sucipto)

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