Explanation

Shifted hyperbola (horizontal):
(x − h)²/a² − (y − k)²/b² = 1

Shifted hyperbola (vertical):
(y − k)²/a² − (x − h)²/b² = 1

Where:

• Center = (h, k)

Asymptotes:
y − k = ±(b/a)(x − h)

Shifting moves the graph but does not change its shape.

Quiz

1. What is the center of (x − 2)²/9 − (y + 1)²/4 = 1?

2. What do h and k represent?

3. Does shifting change the asymptotes’ slopes?

4. What form opens left/right?

5. Are asymptotes important for graphing?

Answer Key

1. (2, −1)

2. Center coordinates

3. No

4. (x − h)²/a² − (y − k)²/b² = 1

5. Yes