Chapter 10 - Section 10.2 - The Ellipse and the Hyperbola - Exercise Set - Page 618: 29

See graph

$$4(x-1)^2+9(y+2)^2=36$$ $$\frac{(x-1)^2}{9}+\frac{(y+2)^2}{4}=1$$ This is an ellipse. The center is (1,-2). The vertices are 3 units away from the center in the x-direction: (4,-2) and (-2,-2). The covertices are 2 unit away from the center in the y-direction: (1,0) and (1,-4). Plot these points and connect with a smooth ellipse.