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equation of a circle

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2 Answers

x2 + y2 - 6x + 8y = 0
 
rearrange the equation:
 
x2 - 6x + y2 + 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
 
(a ± b)2 = a2 + 2ab + b2  

Standard form for the equation of the circle is 
(x -a)2 + (y - b)2 = r2

Distance between two poins on the coordinate plane is: 
d = √[(x1 - x2)2 + (y1- y2)2]    
 
 
~~~~~~~~~~~  

x2 + y2 - 6x + 8y = 0

(x2 - 2*3*x + 9) + (y2 + 2*4*y + 16) = 9 + 16

(x - 3)2 + (y + 4)2 = 52  

and coordinates of the central are (3, - 4) and coordinates of origin are (0, 0), the 
distance from the central to the origin is: 

d = √(x2 + y2) = √25 = 5