Question

the graph shows an ellipse. what are its co - vertices?

Explanation:

Step1: Recall the definition of co - vertices of an ellipse

For an ellipse centered at the origin \((0,0)\) of the form \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}} = 1\) (\(a>b>0\)), the vertices are \((0,\pm a)\) and the co - vertices are \((\pm b,0)\). In a graph, co - vertices are the points where the ellipse intersects the minor axis.

Step2: Identify the intersection points of the ellipse with the \(x\) - axis

Looking at the graph of the ellipse centered at the origin \((0,0)\), the ellipse intersects the \(x\) - axis at \((- 1,0)\) and \((1,0)\)

Answer:

\((-1,0)\) and \((1,0)\)