Ok so this is conic sectuion first group x's with x's and y's with y's then complete the squra with x's and y's
2x^2-8x+2y^2+10y+2=0 2(x^2-4x)+2(y^2+5y)+2=0 take 1/2 of linear coeficient and square -4/2=-2, (-2)^2=4 5/2=2.5, 2.5^2=6.25 add that and negative inside
2(x^2-4x+4-4)+2(y^2+5y+6.25-6.25)+2=0 factor perfect squares 2((x-2)^2-4)+2((y+2.5)^2-6.25)+2=0 distribute 2(x-2)^2-8+2(y+2.5)^2-12.5+2=0 2(x-2)^2+2(y+2.5)^2-18.5=0 add 18.5 both sides 2(x-2)^2+2(y+2.5)^2=18.5 divide both sides by 2 (x-2)^2+(y+2.5)^2=9.25
that is a circle center (2,-2.5) with radius √9.25
