Question

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)

Answer 1

Answer: D (6,-3)

Step-by-step explanation: I took the quiz

Answer 2

We have been given an equation of hyperbola
`((y+3)^2)/(81)-((x-6)^2)/(89)=1`. We are asked to find the center of hyperbola.

We know that standard equation of a vertical hyperbola is in form
`((y-k)^2)/(b^2)-((x-h)^2)/(a^2)=1`, 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:

`((y-(-3))^2)/(81)-((x-6)^2)/(89)=1`

Now we can see that value of k is
`-3`. Therefore, the vertex of given hyperbola will be at point
`(6,-3)` and option D is the correct choice.