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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)

2 Answers

6 votes

Answer: D (6,-3)

Step-by-step explanation: I took the quiz

7 votes

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.

User Acenturyandabit
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