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im having trouble with some math problems can you help

the question is write the equation of the hyperbola with the given foci and vertices.  foci:(6,0), (-6,0)  vertices: (4,0)(-4,0)

Hi Sam;
(4,0)(-4,0)
Are these the vertices or the x-intercepts?
A parabola can only have one vertex.
It can have two x-intercepts.
Vivian, it's a hyperbola, not a parabola.

Hello,

This is an East - West hyperbola centered at the origin.    The standard form is (x/a)2 - (y/b)2 = 1

With this standard form, the distance from the center to a vertex is a , so   a = 4.    The distance from the center to a focal point is:
sqrt( a2 + b2)   ,  so    6 =  sqrt( 16 + b2)  .    Solving this for b  results in b =  sqrt(20).

Plugging these values for a and b into the standard form results in
(x/4)2 - (y/sqrt(20))2  = 1

The only practical way to deal with hyperbola or ellipse problems like this one is to memorize the formulas for  standard forms and distances to vertex, foci and directrix.