write the equation of the conic section shown below.\nanswer\nanswer:

Explanation:

Step1: Identify ellipse center

From the graph, the center $(h,k)$ is $(-4,1)$.

Step2: Find semi-major/minor axes

Horizontal semi-axis $a$: Distance from center to leftmost point $(-9,1)$ is $|-9 - (-4)| = 5$. Vertical semi-axis $b$: Distance from center to top point $(-4,5)$ is $|5 - 1| = 4$.

Step3: Write ellipse standard form

Use horizontal ellipse formula: $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$. Substitute $h=-4, k=1, a=5, b=4$: $\frac{(x-(-4))^2}{5^2} + \frac{(y-1)^2}{4^2} = 1$ Simplify signs and squares: $\frac{(x+4)^2}{25} + \frac{(y-1)^2}{16} = 1$

Answer:

$\frac{(x+4)^2}{25} + \frac{(y-1)^2}{16} = 1$