Question

Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.

Answer 1

we have that
2x² + 9y² = 18------> divided by 18
so
2x² /18+ 9y²/18 = 18/18------> x/9² + y²/2 = 1

Part a)
the equation of the ellipse if of the form
(x-h)²/a²+(y-k)²/b²=1
where (h,k) is the center
in this problem
(h,k) is (0,0) ------> is the origin
a²=9------> a=3
b²=2-----> b=√2

Part b)
vertices are
(h+a,k) and (h-a,k)
(0+3,0)-----> (3,0)
(0-3,0)----> (-3,0)

Part c)
foci are
(h+c.k) and (h-c, k)
where
c²=a²-b²-----> c²=9-2-----> c²=7-----> c=√7

the foci are
(0+√7, 0)-----> (√7,0)
(0-√7,0)------> (-√7,0)