Which is the equation of an ellipse centered at the origin with foci on x-axis, major axis of length 12 and minor axis of length 8?

Step-by-step explanation:

Center of the ellipse is at origin (0, 0)

So (h, k) = (0, 0)

Length of major axis = 12

2a = 12

⇒ a = 6

Length of minor axis = 8

⇒ 2b = 8

⇒ b = 4

Since focus is on the x-axis, so it's a horizontal ellipse.

Equation of the horizontal ellipse is in the form of,

By substituting the given values of a, b, and (h, k)

h is the x-coordinate of the vertex

step-by-step explanation:

we have

in this function

the point represent the vertex of the function

so

h is the x-coordinate of the vertex

k is the y-coordinate of the vertex