Kamis, 01 Januari 2015

Lingkaran

Persamaan lingkaran merupakan suatu persamaan yang membentuk lingkaran pada koordinat Cartesius.
Persamaan lingkaran yang berpusat di O(0,0)  dan berjari-jari r adalah x^2 + y^2 = r
Bentuk Umum Persamaan Lingkaran
Jika kita menjabarkan persamaan  (x-a)^2 + (y-b)^2 = r^2 akan didapat:
x^2 + y^2 - 2ax - 2by + a^2 + b^2 - r^2 = 0
Dengan mensubstitusikan A = -2a, B = -2b, dan C = a^2 + b^2 - r^2, persamaan tersebut menjadi:
x^2 + y^2 + Ax + By + C = 0
Ini merupakan bentuk umum persamaan lingkaran yang berpusat di titik P(a,b)  dan jari-jari r.
Jari-jari lingkaran tersebut adalah r = \sqrt{\frac{1}{4} A^2 + \frac{1}{4} B^2 - C} dan pusatnya  (-\frac{1}{2}A, -\frac{1}{2}B)

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