Find the standard form of the equation of the circle with the given characteristics. Center at origin; radius: 4√2

x^2 + y^2 = 32

Step-by-step explanation:

The fact that the circle's center is at (0,0) tells you that the circles equation is of the form x^2 + y^2 = radius^2

radius = 4*sqrt (2) Given

r^2 = (4sqrt (2)) ^2

r^2 = 16 * 2

r^2 = 32

So the entire equation is

x^2 + y^2 = 32