Question

question 4 of 10
what is the length of the major axis of the ellipse shown below?
\\(\frac{(x - 1)^2}{9}+\frac{(y + 5)^2}{16}=1\\)
a. 32
b. 16
c. 4
d. 8

Explanation:

Step1: Identify the form of the ellipse equation

The standard - form of an ellipse equation is $\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1$. For the given equation $\frac{(x - 1)^2}{9}+\frac{(y + 5)^2}{16}=1$, we have $a^2 = 9$ (so $a = 3$) and $b^2=16$ (so $b = 4$). Since $b>a$, the major - axis is vertical.

Step2: Recall the formula for the length of the major axis

The length of the major axis of an ellipse is given by $2b$ when the major axis is vertical.
Since $b = 4$, then $2b=8$.

Answer:

D. 8