find the centre of a circle

Question

find the center of the circle, please show step by step

 

4x²+10x+4y²+10y-2=0

Answer 1

4x² + 10x +4y² + 10y - 2 = 0

 

Add 2 to both sides:

4x² + 10x +4y² + 10y = 2

 

 

Divide both sides by 4:

4x²/4 + 10x/4 + 4y²/4 + 10y/4 = 2/4

 

x² + 5x/2 + y² + 5y/2 = 2/4

 

Complete the square for x...

 

(x² + 5x/2      )  + (y² + 5y/2     )  = 2/4

 

Divide 5/2 by 2 and square it.

 

(x² + 5x/2 + 25/16)   + (y² + 5y/2   ) = 2/4 + 25/16

 

 

Same for y:

 

(x² + 5x/2 + 25/16) + (y² + 5y/2 + 25/16 ) = 8/16 + 25/16 +25/16

 

Simplify:

 

 

(x + 5/4)² + (y + 5/4)² = 8/16 + 50/16 = 58/16 = 29/8

 

(x + 5/4)² + (y + 5/4)² = 29/8

 

 

 

Center of the circle is (-5/4, -5/4) or (-1.25, -1.25).

 

The radius would be sqrt(29/8) or sqrt(3.625) = √58/4 ≈ 1.904

 

 

Sqrt(29)         sqrt(2)   = sqrt(58)

--------      *   -------        -----------

2 (sqrt(2))      sqrt(2)           4