Find the center and the radius

Question

x^2+6x+y^2+8y+9=0

Answer 1

Standard Equation for a circle:

 

(x -h)² + (y-k)² = r²

 

where (h,k) = center

and r= radius

 

 

x²+6x+y²+8y+9=0

 

Start by grouping like terms, add a (b/2)² term to both sides of equal sign to complete the square

 

 

(x² + 6x + (6/2)² ) + (y² + 8y + (8/2)² ) + 9 = (6/2)² + (8/2)² 

 

move constants (the 9) to the other side of the equal sign by +/- them.

 

(x² + 6x + 9) + (y² + 8y + 16)  = 9 + 16 - 9

 

(x + 3)² + (y + 4)² = 16

 

Compare this to standard circle equation:

 

(x - h)² + (y - k)² = r²

 

(x - (-3))² + (y -(-4))² = (4)²