equation of a circle

Question

write the equation of the circle x²+y²-6x+8y=0 in the standard form. Find the radius of the circle and the distance from the center to the origin

Answer 1

(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

Answer 2

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