Question

which of the following is the graph of the ellipse shown below?
\\(\frac{(x + 2)^2}{25}+\frac{(y - 5)^2}{9}=1\\)

Explanation:

Step1: Identify the center of the ellipse

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. For the given ellipse $\frac{(x + 2)^2}{25}+\frac{(y - 5)^2}{9}=1$, we have $h=-2$ and $k = 5$, so the center is $(-2,5)$.

Step2: Identify the semi - axes

We have $a^2 = 25$, so $a = 5$ (semi - major axis along the x - related part if $a>b$) and $b^2=9$, so $b = 3$ (semi - minor axis).

Step3: Analyze the options

We check which graph has a center at $(-2,5)$.

• Option A: The center is not at $(-2,5)$.
• Option B: The center is at $(-2,5)$.
• Option C: The center is not at $(-2,5)$.
• Option D: The center is not at $(-2,5)$.

Answer:

B.