What type of conic section does the following equation give

What type of conic section does the following equation give? 2x^2 - 4x + 2y^2 + 4y + 5 = 0

Solution

2x^2 -4x +2y^2 +4y +5 =0

seaparating x and y termms :

( 2x^2 -4x ) + (2y^2 +4y ) +5 =0

2(x^2 -2x) +2(y^2 +2y) +5 =0

2(x-1)^2 -2 +2(y+1)^2 -2 +5 =0

2(x-1)^2 + 2(y+1)^2 +1 =0

2(x-1)^2 + 2(y+1)^2 = -1

(x-1)^2 + (y+1)^2 = -1/2

It represents none of the conic equations.