Question

Can someone help me with this problem? Please

Answer 1

Semicircle g has center at (-4,0) and radius 2.

Use the general equation for a circle:

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

Here, the center is (h,k), where h = -4 and k=0.  Also, r = 2

So we have (x-[-4])^2 + (y-0)^2 = r^2 = 4

Let's solve for y in terms of x:

y^2 = 4 - (x+4)^2 

Since we are interested in only the bottom half of this circle,

y  =  - sqrt(4 - x^2 - 8x - 16)