Answer
Ellipse
vertices: (1±√2,2)
foci: (1±1,2)
center: (1,2)
Work Step by Step
x²-2x+2y²-8y= -7
(x-1)²-1+2(y²-4y)= -7
(x-1)²-1+2( (y-2)²-4)= -7
(x-1)²-1+2(y-2)²-8= -7
(x-1)²+2(y-2)²=2
((x-1)²/2)+((y-2)²/1) = 1
from the equation a=√2, b=1
and c = 1 from c²= a²-b²
from the equation the center (h,k)=(1,2)
and vertices (h±a,k) = (1±√2,2)
and foci (h±c,k)= (1±1,2)
