Question

question 6 of 10
what are the coordinates of the center of the ellipse shown below?
\\(\frac{(x - 1)^2}{9}+\frac{(y + 5)^2}{16}=1\\)
a. (3,4)
b. (5,-1)
c. (-3,-4)
d. (1,-5)

Explanation:

Step1: Recall ellipse standard - form

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

Step2: Identify $h$ and $k$ values

For the given ellipse $\frac{(x - 1)^2}{9}+\frac{(y+5)^2}{16}=1$, we can rewrite the second - term as $\frac{(y-(- 5))^2}{16}$. Here $h = 1$ and $k=-5$.

Answer:

D. $(1,-5)$