Final answer:
To find the equation of the ellipse, we can use the standard form equation x^2/a^2 + y^2/b^2 = 1. Given that the ellipse passes through the point (2, 1) and has a minor axis of 4, we can substitute these values to find the equation.
Step-by-step explanation:
An ellipse is a closed curve in which the sum of the distances from any point on the curve to the two foci is a constant. To determine the equation of an ellipse centered at (0, 0), we can use the standard form equation:
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. Given that the ellipse passes through the point (2, 1) and has a minor axis of 4, we can substitute these values to find the equation.
First, we know that the midpoint of the minor axis is (0, 0) and the length of the minor axis is 4. Therefore, the length of the semi-minor axis 'b' is 2. Next, we can use the point (2, 1) to find the value of 'a'.
Using the formula:
(2/a)^2 + (1/2)^2 = 1
Solving for 'a', we get:
a = 4/√3
Using these values of 'a' and 'b', the equation of the ellipse is:
x^2/(16/3) + y^2/4 = 1