Question

For the equation 9x^2+4y^2+54x-8y+49=0 determine the center, vertices and foci?

Answer 1

rearrange stuff and complete the squares:

9x^2+54x + 4y^2-8y = -49
9(x^2+6x) + 4(y^2-2y) = -49
9(x^2+6x+9) + 4(y^2-2y+1) = -49 + 9*9 + 4*1
9(x+3)^2 + 4(y-1)^2 = 36

(x+3)^2/4 + (y-1)^2/9 = 1

Now answer the questions.

Answer 2

how do you determine vertices?

Answer 3

for this ellipse, the major axis is vertical.
a = 3
b = 2
The vertices are at (-3,1±3)
The co-vertices are at (-3±2,1)

Looks like it's time to review your ellipses.