What is the equation for a half a circle?

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Answer 1 · 2016-04-08T19:38:26

In polar co-ordinates, r = a and $alpha < theta < alpha+pi$ .

The polar equation of a full circle, referred to its center as pole, is r = a. The range for $theta$ for the full circle is $pi$ .

For half circle, the range for $theta$ is restricted to $pi$ .

So, the answer is
r = a and $alpha < theta < alpha + pi$ , where a and $alpha$ are constants for the chosen half circle.

Answer 2 · 2016-04-08T20:35:35

In rectangular coordinates, the equation of the upper half of a circle can be written:

$y = sqrt(r^2 - (x-h)^2) + k$

The equation of a full circle with centre $(h, k)$ and radius $r$ can be written:

$(x-h)^2+(y-k)^2 = r^2$

Hence the upper half of a circle can be expressed as:

$y = sqrt(r^2 - (x-h)^2) + k$

where $(h, k)$ is the centre and $r$ the radius.