Thread: Equation of a half circle

Find an expression for the for the function whose graph is the given curve. Give the domain and range.

The bottom half of the circle whose center is @(3,0) and has a radius of length 5.



I'm so lost.

Here is the equation of the whole circle.



Now find y1 and y2, the negative square root would be the botom half of the circle.

Regards.

Lets find the equation of the full circle first.


This is


Rearrange for Y

This is

When it is in this form, the range and domain are defined as follows:
The domain is all possible values that x can take
The range is all possible values that y can take


Because it is a circle with radius 5, centered around (3,0); you know the domain and range are:
Domain:
Range:



You want the bottom half of the circle, which is the part where Y<0.
Hopefully, you can see that
Domain: (the same)
Range: (bottom half only)


This is much easier to draw than do in your head. I'll try to attach an image later



edit too slow

I got the same answer as SpringFan25.