Question

question 1 of 20
what is the length of the major axis of the conic section shown below?
\\(\frac{(x - 2)^2}{4}+\frac{(y + 5)^2}{9}=1\\)

Explanation:

Step1: Identify the form of the ellipse

The equation $\frac{(x - 2)^2}{4}+\frac{(y + 5)^2}{9}=1$ is of the form $\frac{(x - h)^2}{b^2}+\frac{(y - k)^2}{a^2}=1$ (where $(h,k)=(2,-5)$), which represents an ellipse with a vertical major - axis.

Step2: Determine the value of \(a\)

For an ellipse of the form $\frac{(x - h)^2}{b^2}+\frac{(y - k)^2}{a^2}=1$, we have $a^2 = 9$, so $a = 3$.

Step3: Calculate the length of the major axis

The length of the major axis of an ellipse is given by $2a$. Since $a = 3$, the length of the major axis is $2\times3=6$.

Answer:

6