# Vertical chords of a hyperbola

Calculus Level 5

If the average length of all the vertical chords of the hyperbola

$$\displaystyle \dfrac{x^2}{9} - \dfrac{y^2}{4} = 1$$

over the interval $$x \in (3,6)$$ is

$$\large \displaystyle a[b \sqrt{c} - \ln(b + \sqrt{c})]$$,

find $$a+b+c$$

Details

• $$c$$ is square free.
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