### Home > PC3 > Chapter 10 > Lesson 10.2.2 > Problem10-127

10-127.

Which of the following equations is the equation of a hyperbola? How can you tell? What is the shape of the graph of the other equation? After you have decided on the shapes, sketch their graphs.

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

Since the terms are being added, this is an ellipse. The center is at $(1, −2)$.

The 'horizontal radius' is $3$ and the 'vertical radius' is $2$.

1. $\frac { ( y - 3 ) ^ { 2 } } { 16 } - \frac { ( x + 2 ) ^ { 2 } } { 25 }= 1$

Since the terms are being subtracted, this is a hyperbola. The center is at $(−2, 3)$.

To create the "box", use a 'horizontal radius' of $5$ and a 'vertical radius' of $4$.