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?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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