write the equation in standard form for the circle passing through (0,8) centered at the origin

Answer 1

The general equation for a circle centered at the origin is:

x^2 + y^2 = r^2

where r is the radius of the circle. We know that this circle passes through (0,8), so we can substitute those values to get:

0^2 + 8^2 = r^2
64 = r^2

Now we can substitute this value of r^2 into the equation and simplify:

x^2 + y^2 = 64

This is the standard form equation for the circle passing through (0,8) and centered at the origin.