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A cooling tower has a cross-section in the shape of the two branches of x²/9 - y²/16 = 1, with…

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A cooling tower has a cross-section in the shape of the two branches of $\dfrac{x^2}{9} - \dfrac{y^2}{16} = 1$ , with lengths in decimetres. Find the eccentricity, the slope of an asymptote and the length of the latus rectum.

Need a reminder? The key ideaShow

A hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ has $c = \sqrt{a^2 + b^2}$ , $e = \dfrac{c}{a}$ , foci $(\pm c, 0)$ , asymptotes $y = \pm\dfrac{b}{a}x$ , latus rectum $\dfrac{2b^2}{a}$ , and $|PF_1 - PF_2| = 2a$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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