Final answer:
The equation of an ellipse centered at the origin with a horizontal major axis of 12 units and a vertical minor axis of 6 units is (x^2/36) + (y^2/9) = 1; where the semi-major axis is 6 units and the semi-minor axis is 3 units.
Step-by-step explanation:
To find the equation of an ellipse centered at the origin with a horizontal major axis of 12 units and a vertical minor axis of 6 units, we first need to identify the lengths of the semi-major axis (a) and the semi-minor axis (b). The semi-major axis is half the length of the major axis, and the semi-minor axis is half the length of the minor axis.
In this case, the semi-major axis (a) is 12 / 2 = 6 units, and the semi-minor axis (b) is 6 / 2 = 3 units. The standard form of the equation for an ellipse centered at the origin is (x^2/a^2) + (y^2/b^2) = 1, where a is the length of the semi-major axis and b is the length of the semi-minor axis.
Plugging our values into this formula, we get (x^2/6^2) + (y^2/3^2) = 1, which simplifies to (x^2/36) + (y^2/9) = 1. This is the equation of the ellipse.