# What are co-vertices in r/o an ellipse?

Feb 14, 2017

Co-vertices are the endpoints of the minor axis .

#### Explanation:

Co-vertices are the endpoints of the minor axis .

Let us consider an ellipse described by ${x}^{2} / 16 + {y}^{2} / 9 = 1$. This is shown below:
graph{x^2/16+y^2/9=1 [-10, 10, -5, 5]}
This is an ellipse with horizontal orientation and as can be seen its co-vertices are $\left(0 , 3\right)$ and $\left(0 , - 3\right)$.

Now consider another ellipse ${\left(x + 3\right)}^{2} / 9 + {\left(y - 4\right)}^{2} / 25 = 1$
graph{(x+3)^2/9+(y-4)^2/25=1 [-12.34, 7.66, -1, 9]}
This is an ellipse with vertical orientation and as can be seen its co-vertices are $\left(- 6 , 4\right)$ and $\left(0 , 4\right)$.