Answer
See graph
Work Step by Step
Following the standard form of an ellipse $x$-axis which is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$:
$$\frac{(x-2)^2}{2^2}+\frac{(y-(-1))^2}{3^2}=1$$ $$(h,k)=(2,-1),a=2,b=3$$
Finding the vertices with major axis the $y-axis$:
$$(h,k+b)=(2,-1+3)=(2,2)$$ $$(h,k-b)=(2,-1-3)=(2,-4)$$
Finding the co-vertices with minor axis the $x-axis$:
$$(h-a,k)=(2-2,-1)=(0,-1)$$ $$(h+a,k)=(2+2,-1)=(4,-1)$$
Plot the center and the vertices.
Draw a smooth curve passing the vertices.
Thus, the sketch of the conics is as shown.
