Question

what is the length of the major axis of the ellipse $\frac{x^{2}}{49}+\frac{y^{2}}{7}=1$? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall the standard form of an ellipse

The standard form of an ellipse is \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1\) (\(a>b>0\)). Here, \(a^{2}=49\), so \(a = 7\), \(b^{2}=7\), so \(b=\sqrt{7}\).

Step2: Determine the length of the major axis

For the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) (\(a > b\)), the length of the major axis is \(2a\).
Since \(a = 7\), then \(2a=14\).

Answer:

\(14\)