Question

I really need helppppp

Answer 1

Answer:

The correct answer is C.

Step-by-step explanation:

In the equation of a circle, if the variable $x$ and $y$ are added or subtracted by any number before being squared, the entire circle with be translated in the opposite amount that was added or subtracted to the circle. For example, $(x-8)^2 + (y-8)^2$ shifts the center 8 to the right and up of the origin, $(x+1)^2+(y+4)^2$ shifts the center 1 to the left and 4 down of the origin. Since the circle represented in the graph is centered directly on the origin, that means the equation will have $x^2+y^2$, which helps you eliminate choices A and C. For the equation of a circle, the radius is the value of the constant on the right side of the equal sign taken to its square root. Since the radius of this circle is 8, that means the constant at the right side of the circle would be 64 or $8^2$, so the correct answer would be choice C: $x^2+y^2=8^2$.