42 lines
1.5 KiB
Markdown
42 lines
1.5 KiB
Markdown
---
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title: Circle Equations
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---
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## Circle Equations
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![Circle centered at (x0, y0) with radius r, a point P(x, y) on the circle, and angle t](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_2.gif)
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### 1. Centre-radius form:
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Circle having centre <i><b>(x<sub>0</sub>, y<sub>0</sub>)</b></i> and radius <b><i>r</i></b>.
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The equation of the circle can be represented as:
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![(x-x0)^2 + (y-y0)^2 = r^2](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_3.png)
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#### General Equation of a Circle:
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![x^2 + y^2 + 2gx + 2fy + c = 0](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_6.png)
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where, `g`, `f`, and `c` are constants.
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Therefore,
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![x0 = (-g), y0 = (-f), and r = square root of (g^2 + f^2 -c)](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_9.png)
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### 2. Parametric form:
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Circle having centre <i><b>(x<sub>0</sub>, y<sub>0</sub>)</b></i> and radius makes an angle <b><i>t</i></b> with the positive direction of <i>x-axis</i>, then <b><i>t</i></b> is called the `parameter`.
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The equation of the circle can be represented as:
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![x = x0 + rcos(t), y = y0 + rsin(t)](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_4.png)
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for,
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![0<=t<= 2 pi](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_5.png)
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### More Information:
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<a href = "http://mypages.valdosta.edu/alazari/math1111/Circle.html" target="_blank" rel="nofollow">Equation of a Circle</a>
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