write the equation of the circle x^{2}+y^{2}-6x+8y=0 in the standard form. Find the radius of the circle and the distance from the center to the origin
x^{2 }+ y^{2 }- 6x + 8y = 0
rearrange the equation:
x^{2 }- 6x + y^{2} + 8y = 0
we use completing the square:
(x - 3)^{2} + (y + 4)^{2} = 9 + 16 = 25
so, radius is √25 or 5
also, distance from center to origin is also 5