How do you write an equation for a hyperbola with Vertices (-6,0) and (6,0) and Foci (- square root 85,0) and ( square root 85,0) What does a, b, and c equal?

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Answer 1 · 2018-04-13T12:26:05

#a=6,b=7,c=sqrt 85#. The equation of hyperbola is
#x^2/36- y^2/49=1#

Vertices are # (-6,0) and (6,0)#

Foci are # (-sqrt 85 , 0) and (sqrt 85,0)#

By the Midpoint Formula, the center of the hyperbola occurs at the

point #(0,0); h=0, k=0 :. a= 6-0=6; a^2=36# ;

# c= sqrt 85. c^2= 85#

#b^2= c^2-a^2=85-36=49 :. b=+-7#

So, the hyperbola has a horizontal transverse axis and standard

form of the equation is #(x-h)^2/a^2-(y-k)^2/b^2=1# or

#(x-0)^2/6^2-(y-0)^2/7^2=1 or x^2/36- y^2/49=1#

graph{x^2/36-y^2/49=1 [-10, 10, -5, 5]}