Answer
The graph is an ellipse with center at $(-3,4)$, major axis at $(-3,9)$ and $(-3,-1)$, and minor axis at $(-6,4)$ and $(0,4)$.
Work Step by Step
The graph of an equation of the form $$\frac{(x-h)^{2}}{b^{2}}-\frac{(y-k)^{2}}{a^{2}} =1 $$is an ellipse with center $(0,0)$.
The x-intercepts are at points $(a,0)$ and $(-a,0)$ and the y-intercepts are at points $(0,b)$ and $(0,-b)$.
Hence, the equation $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-4\right)^2}{25}=1$$ has a center point at $(-3,4)$.
Since the larger number is under the $y$, then the graph will be a vertical ellipse. So, $$b = \sqrt 9$$ $$= 3$$ and $$a = \sqrt {25}$$ $$= 5$$.
We can now use $a$ and $b$ to plot the ends of the major and minor axis. The value of $b (3)$ is the distance from the center point $(-3,4)$ to the end of the minor axis $(-6,4)$ and $(0,4)$.
On the other hand, the value of $a (5)$ will be the distance from the center to the end of the major axis $(-3,9)$ and $(-3,-1)$. The resulting graph will then be:
