The equation of an ellipse is x^2/16+y^2/36=1and the ellipse is centered at the origin. find the vertices of the major axis and determine whether the ellipse has a horizontal or vertical major axis.

The form of an eclipse is written as:

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

Matching the values in the given equation tot he form of an eclipse you have:

a = 6

b = 4

k = 0

h = 0

A is the radius of the major axis and b is the radius of the minor axis.

H is the X offset and K is the Y offset.

The first vertex is written as (h, k+a)

Replacing the letters with their values you get:

(0, 0+6) = (0,6)

The second vertex is written as (h, k-a)

Replacing the letters with their values you get:

(0, 0-6) = (0,-6)

The vertices of the are (0,6) and (0,-6)

The vertices are the end points of the major axis, since 6 and -6 are longer than the minor axis of -4, 4 the ellipse has a vertical major axis

step-by-step explanation:

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