3. could the circle with equation x^2−6x+y^2−7=0 have a radius of 4? why or why not?

Yes, it has a radius of 4

Step-by-step explanation:

General equation of a circle is

x²+y²+2gx+2fy+c = 0... 1

Where r = √g²+f²-c

Comparing the general b equation to the given equation to get g, f and c

x^2−6x+y^2−7=0

Rearranging

x²+y²-6x -7 = 0... 2

Comparing 1 and 2;

2gx = -6x

2g = -6

g = -3

2fy = 0 ( since there is no function of y in the given equation)

f = 0

c = -7

Substituting into the radius formula

r = √(-3)²+0² -(-7)

r = √9+7

r = √16 units

r = 4units

It is true that the radius of the circle is 4units