An ellipse centered at the origin with vertices at (±a, 0) and co-vertices at (0, ±b) can be expressed in the standard form of the equation:
Standard Form: \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
In this case, the vertex is given as (6, 0) and the co-vertex as (0, 4). Here, we can see that:
- The distance from the center to the vertex (a) is 6.
- The distance from the center to the co-vertex (b) is 4.
We can find the values of a and b as follows:
- a = 6
- b = 4
Next, we square these values to substitute them into the equation:
- a² = 6² = 36
- b² = 4² = 16
Substituting these values into the standard form of the ellipse equation, we get:
\[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \]
This is the equation in standard form of the ellipse centered at the origin with the specified vertices.