College Algebra Question?

Question

Find the center, vertices, and foci of the ellipse.

9x to the 2nd power + 25y to the second power + 162x + 300y +1404 = 0

I'm not sure how to show work for this problem. Help and work shown is greatly appreciated. Thanks.

Answer 1

9x^2 + 162x + 25y^2 +300y = 1404
9(x^2+18x+81)+25(y^2+12y+36) = -1404+729+900
9(x+3)^2 + 25(y+6)^2= 225
(x+3)^2/25 + (y+6)^2/9 = 1

center = (-3,-6)
vertex = (2,-6) (-8,-6)
foci = (1,-6) (-4,-6)