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

Answer: 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