Answer
See graph
Work Step by Step
Following the standard form of a hyperbola with major axis of $x$-axis which is $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$:
$$\frac{(x-(-3))^2}{4^2}-\frac{(y-(-4))^2}{5^2}=1$$ $$(h,k)=(-3,-4),a=4,b=5$$
Finding the vertices:
$$(h+a,k)=(-3+4,-4)=(1,-4)$$ $$(h-a,k)=(-3-4,-4)=(-7,-4)$$
Plot the center and the lengths of $a$ and $b$.
Draw a box and the lines passing through the corners of the box as shown. These two lines are the asymptotes of the graph.
Plot the two vertices.
Draw smooth curves each passing a vertex and approaches the asymptotes.
Thus, the sketch of the conics is as shown.
