Algebra 2!!

Question

Identify the constant difference for a hyperbola with foci (0, −5) and (0, 5) and a point on the hyperbola (0, 3).

Answer 1

With the given foci the transverse axis is vertical. That means the vertices of the hyperbola lie on the line x = 0. The midpoint of the segment joining the foci is (0,0) and that is the center of the hyperbola. A point that is on the graph of the hyperbola, given as (0,3) lies on the transverse axis, so the point (0,3) must be a vertex. That means that "a" has a value of 3 (the distance from the center to one of the vertices). The constant difference for a hyperbola is 2a. The constant difference is the difference between the distances from a point on the hyperbola to the foci. In this case that difference is 2(3) = 6.

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