The conic equation is
.
Rewrite the equation by completing the squares method.
\
Compare it to standard form of vertical ellipse is
.
Thus, graph of the equation represents an ellipse.
\
is length of semi major axis and
is length of semi minor axis.
Center is
.
vertices
.
Foci
.
.
Substitute
and
.

.
Foci :
.
(a) The graph of the equation represents an ellipse.
\(b) Vertices
and Foci
.