Question

what is the length of the major axis of the ellipse shown below?\\(\frac{(x + 2)^2}{9} + \frac{(y - 4)^2}{36} = 1\\)\
\\(\bigcirc\\) 12\
\\(\bigcirc\\) 36\
\\(\bigcirc\\) 18\
\\(\bigcirc\\) 6

Explanation:

Step1: Recall the standard form of an ellipse

The standard form of an ellipse is \(\frac{(x - h)^{2}}{b^{2}}+\frac{(y - k)^{2}}{a^{2}} = 1\) (\(a>b>0\)), where the length of the major axis is \(2a\).

Step2: Identify \(a^{2}\) in the given equation

In the equation \(\frac{(x + 2)^{2}}{9}+\frac{(y - 4)^{2}}{36}=1\), we have \(a^{2}=36\). Then \(a = 6\).

Step3: Calculate the length of the major axis

The length of the major axis is \(2a\). Substituting \(a = 6\), we get \(2\times6=12\).

Answer:

12