How do you graph half a circle on a coordinate plane?

Question

I know that the equation for the graph of a circle is
(x-something)^2 + (y-someting)^2=r^2

But how do you graph to get, lets say, the bottom half of it? Do you divide it by two or is it more complicated? Help please! This Pre-Calc is crazy.

And would negating it make it right side up or upside down?

In the problem it is already graphed with the center at (3,-3) and the bottom half of the circle. I have to determine how they actually just got that part and why not the top, left, or roght halves.

Answer 1

The general equation for a circle is (x-a)^2 + (y-b)^2 = r^2
the center of the circle is at coordinates (a,b) and it has the radius r. even with a coordinate plane, I would use a compass to draw (graph) the circle, as few points on a circle are at the coordinate intersections.

To draw the bottom half, start drawing at (a ± r, b) and swing your compass down and around until you come back to the line y = b. r remains the same, and the center point remains The same.

To negate it you would "flip" it about the y = b axis, making it a dome, instead of a bowl.

Answer 2

In fact it is very simple. By the formula you have given above plot the (x,y). This represents the centre of the circle. r represents the radius of the circle. So by plotting the centre and drawing a few line ouwards from the centre of lenght r you can actually plot the circle.

Answer 3

I Graph to the Right continuing with the time line. It will look like a half moon in the sky.