Final answer:
The standard form of the equation for an ellipse with a horizontal major axis that passes through (8, 0) and (0, 2) is (x^2/64) + (y^2/4) = 1, where the semi-major axis is 8 units and the semi-minor axis is 2 units.
Step-by-step explanation:
To find the standard form of the equation of an ellipse with a horizontal major axis that passes through the points (8, 0) and (0, 2), we first need to identify the lengths of the semi-major axis (a) and the semi-minor axis (b). Since the ellipse passes through (8, 0), this indicates that the semi-major axis is 8 units long because the point lies on the major axis. Similarly, the point (0, 2) reveals that the semi-minor axis is 2 units long because it lies on the minor axis.
The standard form for an ellipse with a horizontal major axis is given by (x2/a2) + (y2/b2) = 1, where 'a' is the length of the semi-major axis and 'b' is the length of the semi-minor axis. Plugging in the values we've found, we have a = 8 and b = 2. Therefore, the equation becomes (x2/64) + (y2/4) = 1.