Question

Find the center, vertices, and foci of the ellipse with equation x squared divided by 81 plus y squared divided by 225 equals 1.

rewriting the equation for ease: (x^2 / 81) + (y^2 / 225) = 1

A: Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (0, -9), (0, 9)
B: Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (-9, 0), (9, 0)
C: Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)
D: Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (-12, 0), (12, 0)

Answer 1

Option C

Explanation:

Answer 2

Correct option: C

Explanation:

As the value over y^2 is bigger than the value over x^2, we have a vertical major axis ellipse.

The generic equation of the vertical major axis ellipse is:

(x - h)^2/b^2 + (y - k)^2/a^2 = 1

And we have that:

center = (h,k)

vertices = (h, k+a) and (h, k-a)

foci = (h, k+c) and (h, k-c), where c^2 = a^2 - b^2

Comparing our ellipse (x^2 / 81) + (y^2 / 225) = 1 with the generic equation, we have that:

h = 0, k = 0, a = 15, b = 9, and c = sqrt(225-81) = 12

So we have:

center = (h,k) = (0,0)

vertices = (h, k+a) and (h, k-a) = (0,15) and (0,-15)

foci = (h, k+c) and (h, k-c) = (0,12) and (0,-12)

Correct option: C