Question

Find the center, vertices, and foci of the ellipse with equation 3x^2 + 8y^2 = 24.

Answer 1

first place in standard form:

x^2/8 + y^2/3 = 1

Since a^2 = 8 is greater than b^2 = 3, the major axis is horizontal. So, we have

a^2 = 8
b^2 = 3
c^2 = a^2-b^2 = 5

Now just read off the info you want:

center: (0,0)
foci: (±c,0)
vertices: (±a,0)