Circle Equation

Question

2 x^2+4 x+2 y^2+12 y = 20 is the equation of a circle with and can be written in the general form (x-h)^2 + (y-k)^2 = r^2. Find h, k, and r.

Answer 1

2x² + 4x + 2y² + 12y = 20

 

Divide both sides by 2:

 

x² + 2x + y² + 6y = 10

 

Complete the square for the x terms and the y terms:

 

(x²+2x+(2/2)) + (y²+6x+(6/2)) = 10 + 2/2 + 6/2

 

(x²+2x+1) + (y²+6x+3) = 10 + 1 + 3

 

(x+1)² + (y+3)² = 14

 

(x-(-1))² + (y-(-3))² = 14

 

h = -1, k = -3, r = √14