Circles???????????????????????????

Question

Find the center and radius of x^2+y^2+8y+14=0

Answer 1

The given equation is x²+y²+8y +14 = 0

x²+y²+8y+14 = 0

x²+y²+8y = - 14

Add 16  to each side

x²+ y²+ 8y +16 = -14+16

(x + 0)²+ (y+4)²= 2

Compare the above equation with given formula (x -h)²+ (y -k)² = r²

Hence (h,k) is center and r is radius

Therefore h = 0, k = -4 and  r = √2

Therefore center (h,k) = ( 0, - 4) and radius r = √2.

Answer 2

The given circle equation is x² + y² + 8y  +14 = 0

Add 2 on each side

x² +  y² + 8y + 14 + 2 = 0 + 2

x² + y² + 8y + 16 = 0 + 2

(x + 0)² + (y  -(-4))² =  2

Compare the equation with circle formula (x - h)² + (y - k)² = r²

Here centre is (h , k) and radius is r

h = 0 , k  = -4 , r = √2

centre (h , k) = (0 , -4)

radius r = √2