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-
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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**

Distance between two poins on the coordinate plane is:

d = √[(x

x

(x