How Do You Calculate the Distance Between Vertices of a Hyperbola?

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Homework Statement


Determine the distance D between the vertices of -9x^2+18x+4y^2+24y-9=0


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The Attempt at a Solution


This is an online problem that my calc2 instructor gave us. I can't find anything in my book of this level of difficulty. Any help would be appreciated.
 
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hi muddyjch! :smile:

(try using the X2 icon just above the Reply box :wink:)

have you tried to complete the square to find the centre of the hyperbola?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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