Question

what are the co - vertices of the ellipse \\( \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 30 } = 1 \\)?
write your answer in simplified, rationalized form.
\\( ( square, square ) \\) and \\( ( square, square ) \\)

Explanation:

Step1: Identify the form of the ellipse equation

The standard form of an ellipse is \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}} = 1\) (\(a>b>0\)). For the given equation \(\frac{x^{2}}{9}+\frac{y^{2}}{30}=1\), we have \(b^{2}=9\), so \(b = 3\), and \(a^{2}=30\), so \(a=\sqrt{30}\).

Step2: Recall the location of co - vertices

For an ellipse of the form \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1\), the co - vertices are \((\pm b,0)\)

Answer:

\((3,0)\) and \((- 3,0)\)