Question

question 12 of 30
what is the length of the major axis of the conic section below?
\\(\frac{(x - 3)^2}{81}+\frac{(y + 6)^2}{49}=1\\)
a. 14
b. 18
c. 7
d. 5

Explanation:

Step1: Identify the form of ellipse equation

The standard - form of an ellipse is $\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1$. Given $\frac{(x - 3)^2}{81}+\frac{(y + 6)^2}{49}=1$, we have $a^2 = 81$ and $b^2=49$, so $a = 9$ and $b = 7$.

Step2: Determine the length of the major axis

For an ellipse $\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1$, if $a>b$, the length of the major axis is $2a$. Since $a = 9$, the length of the major axis is $2\times9=18$.

Answer:

B. 18