let equation of an ellipse be x^2+4y^2+6x-8y+9=0

Question

a. Find the standard form of the ellipse
b. Find the center
c. Find the vertices
d. Find the foci
e. Find the eccentricity

Answer 1

x^2+4y^2+6x-8y+9=0
x^2+6x + 4y^2-8y = -9
x^2+6x+9 + 4y^2-8y+4 = -9+9+4
(x+3)^2 + 4(y-1)^2 = 4

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

Now the rest should be easy. Come on back if you get stuck.