What is the center of the hyperbola whose equation is (y+3)^2/81-(x-6)^2/89=1?
A. (-6, 3)
B. (-3, 6)
C. (3, -6)
D. (6, -3)

We have been given an equation of hyperbola . We are asked to find the center of hyperbola.  

We know that standard equation of a vertical hyperbola is in form , where point (h,k) represents center of hyperbola.

Upon comparing our given equation with standard vertical hyperbola, we can see that the value of h is 6.

To find the value of k, we need to rewrite our equation as:

Now we can see that value of k is . Therefore, the vertex of given hyperbola will be at point and option D is the correct choice.

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

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