Find an equation for the hyperbola that satisfies the following conditions. Vertices (1,4) and (7,4); foci 18 units apart .

Question

It has to be in the form 1=

Answer 1

Using the vertices, you can determine the center is half way between them at (4,7)

The distance between the center and vertices is 3, therefore 3 is the a value, so a² is 9.

We and use the information from the focus to find the c value. Since they are 18 units apart, c=18/2 or c=9

c²=a²+b²

9²=3²+b²

81=9+b²

72=b²

All this information can be pulled together to form the equation. The location of the vertices tells you that the traverse axis is horizontal, is is the first term, a2 goes under the x value.

(x-4)² - (y-7)²=1

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9 72