What is the equation for a half a circle?

2 Answers
Apr 8, 2016

Answer:

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

Explanation:

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.

Apr 8, 2016

Answer:

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

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

Explanation:

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.