### Home > A2C > Chapter 11 > Lesson 11.3.1 > Problem11-128

11-128.

For each equation below, identify the shape of the graph, list all of the necessary information, and sketch a graph.

1. $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

What does the parent graph look like? Notice the terms are added.

What is the center? Is the major axis vertical or horizontal?

1. $\left(x − 4\right)^{2} + \left(y + 2\right)^{2} = 25$

This equation has the form (xh)2 + (yk)2 = r2. What is this shape?

What is the center and radius?

1. $\frac { ( y - 2 ) ^ { 2 } } { 36 } - \frac { ( x - 3 ) ^ { 2 } } { 9 } = 1$

What does the parent graph look like? Notice the terms are subtracted.

Find the center, foci, and vertices.

1. $3x + \left(y − 2\right)^{2} = 10$

When you isolate the x term, the equation becomes:

$x=-\frac{1}{3}(y-2)^2+\frac{10}{3}$

This is a sleeping parabola.