Write an equation of the ellipse with center at (0, 0), vertex at (4, 0), and co-vertex at (0, 2)
To write the equation of an ellipse, we need to know its center, vertex, and co-vertex.
For this problem, the center of the ellipse is given as (0, 0), which means the ellipse is centered at the origin. The vertex is given as (4, 0), which tells us that the major axis is along the x-axis and the distance from the center to the vertex is 4 units. The co-vertex is given as (0, 2), which means the minor axis is along the y-axis and the distance from the center to the co-vertex is 2 units.
The equation of an ellipse centered at the origin can be written as:
(x^2/a^2) + (y^2/b^2) = 1
In this equation, 'a' represents the distance from the center to the vertex along the x-axis, and 'b' represents the distance from the center to the co-vertex along the y-axis.
From the given information, we can determine that a = 4 and b = 2.
Substituting these values into the equation, we get:
(x^2/4^2) + (y^2/2^2) = 1
Simplifying, we have:
(x^2/16) + (y^2/4) = 1
Thus, the equation of the ellipse is (x^2/16) + (y^2/4) = 1.