### Home > PC3 > Chapter 10 > Lesson 10.1.3 > Problem10-52

10-52.

Sketch a hyperbola centered at the origin with focal points at $(0, 3)$ and $(0, −3)$. Mark a point $P$ on your hyperbola and label it with the coordinates $(x, y)$.

Your hyperbola should open vertically since the focal points are vertical.

1. Write an expression for the difference of the distances from point P to each of focal points.

Distance from $(0, 3)$ to $(x, y)$:

2. If the difference in the distances from any point on the hyperbola to each focal point is $5$ units, use this distance with your expression from part (a) to create an equation.

3. See how far you can get rewriting your equation from part (b) in graphing form.

Get one of the square roots by itself on one side then square both sides.
Simplify and repeat this process with the square root that still remains.