What is the equation of a hyperbola with vertices at (-3, 0) and (3, 0) and co-vertices (0, 5) and (0, -5).

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First the hyperbola is a horizontal hyperbola because the vertices are at (-3, 0) and (3, 0) whch are horizontal from each other.

The standard equation for a horizontal hyperbola is:

`(x-h)^2/a^2 - (y - k)^2/b^2 = 1` In this form, (h, k) represents the center of hyperbola, the distance from the center to a vertex is "a" and the distance from the center to a co-vertex is "b".

The center is always halfway in between the vertices therefore, the center (h, k) is (0, 0).  Now that we have center, we can find "a" and "b".  

THe distance from the center to either vertex is 3.  So "a" = 3.  THe distance from the center to either co-vertex is 5, so "b" =5.

So substituting in these values we have:

`(x-0)^2/3^2 - (y - 0)^2/5^2 = 1`

which will simplify to your equation of:  `x^2/9 - y^2/25 = 1`  

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