How do I find the equation for a semicircle with a radius of 2 on the x axis? I'm doing a calculus project where we have to make a model of some graph rotated about the y axis. I am doing a fish bowl and I have most of it understood and ready. The only thing I'm not sure of is what the equation of the semicircle is if its center is at (0,1.5). I added a picture to help illustrate it. Thank you for your help. Image of semicircle

Equation of a semi-circle at the origin:
$y= (r^2-x^2)^{1/2}$
To translate this to centre (a, b):
$y = \sqrt{r^2 - (x - a)^2} + b$
The solution for your example SHOULD be:
$y=\sqrt{4-x^2}+1.5$
Except, it's not. The image attached shows this graph, but rotated 90 degrees clockwise.
To resolve this, I'm going to perform a refection in the line y=x. This can be done by swapping the x and y values as shown:
$x=\sqrt{4-y^2}+1.5$
