Sure, let's write the equation of the ellipse using the general form equation for ellipse centered at origin:
The general form of an ellipse centered at origin is given by:
**(x²/a²) + (y²/b²) = 1**
Here, two crucial elements are required. These are the values of 'a' and 'b'.
In an ellipse, 'a' represents the distance from the center to a vertex and ‘b’ represents the distance from the center to a co-vertex.
Given in the question, a vertex is at (4,0). This tells us that the value of 'a' is 4.
Also, it's given that a co-vertex is at (0,2). By observation, it's obvious that the value of 'b' is 2.
Let's substitute these values 'a' and 'b' into our general form of ellipse equation:
Then the equation becomes:
**(x²/4²) + (y²/2²) = 1**
After simplifying it further, it becomes:
**(x²/16) + (y²/4) = 1**
And this is the equation of the ellipse we sought.