Answer:
x² + y² = 80
Explanation:
Pre-Solving
We are given that a circle has the center at the origin (the point (0,0)) and passes through the point (-8,4).
We want to write the equation of this circle in the standard equation. The standard equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.
Solving
As we are given the center, we can plug its values into the equation.
Substitute 0 as h and 0 as k.
(x-0)² + (y-0)² = r²
This becomes:
x² + y² = r²
Now, we need to find r².
As the circle passes through (-8,4), we can use its values to help solve for r².
Substitute -8 as x and 4 as y.
(-8)² + (4)² = r²
64 + 16 = r²
80 = r²
Substitute 80 as r².
x² + y² = 80