To find the equation of this ellipse, we first need to determine the lengths of the major (2a) and minor (2b) axes.
The general form of an equation of an ellipse centered at the origin is represented by: x^2/a^2 + y^2/b^2 = 1.
In this case, a is the x-coordinate of the vertex, and b is the y-coordinate of the co-vertex.
Step 1: Finding the length of the major axis
The major axis is determined by the vertex. Since the vertex of the ellipse is at (9,0), the distance from the center (0,0) to the point (9,0) is 9 units.
Hence, the length of the semi-major axis, a = 9 units.
Step 2: Finding the length of the minor axis
The minor axis is determined by the co-vertex. Since the co-vertex of the ellipse is at the point (0,5), the distance from the center to point (0,5) is 5 units.
Therefore, the length of the semi-minor axis, b = 5 units.
Step 3: Plugging the values into the ellipse equation
Now that we have the lengths of the major (a) and minor (b) axes, we can plug these values into the general form of the equation of an ellipse.
The equation of ellipse now becomes x^2/81 + y^2/25 = 1
In conclusion, the lengths of the major and minor axes of the ellipse with a vertex at (9,0) and a co-vertex at (0,5) are 9 units and 5 units, respectively. And the equation of the ellipse is represented by x^2/81 + y^2/25 = 1.