### Concept (1)

Graphing a transformed hyperbola combines the skills of graphing hyperbolas and graphing transformations. With hyperbola graphs, we use the formula a^2 + b^2 = c^2 to determine the foci and y= + or - (a/b)x to determine the asymptotes. When transforming hyperbola graphs, we find the center of the graph and then graph accordingly.

### Sample Problems (5)

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Graph the equation for a hyperbola with vertices (0,1),(4,1) and foci at (-1,1),(5,1).

###### Problem 1
How to find the equation of a transformed hyperbola given vertices and foci.

Given 4x² − 9y² − 8x − 54y − 113 = 0.

Find the center, vertices, covertices, and focus.
###### Problem 2
How to find information about a hyperbola by completing the square.
###### Problem 3
Writing the equation for a hyperbola that is not centered at the origin from the vertices and foci.
###### Problem 4
Writing the equation for a hyperbola from vertices and foci.
###### Problem 5
Complete the square to move from general to standard form of a hyperbola.