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Eccentricity

Find the leng...

Question

Find the length of latus rectum of the parabola.

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Solution

Let equation of parabola is $y^{2} = 4 a x$
Ends of a focal chord $A (a t^{2}, 2 a t)$ and $B [\frac{a}{t^{2}}, - \frac{2 a}{t}]$
$A B = S A + S B = a t^{2} + a + \frac{a}{t^{2}} + a = a {(t + \frac{1}{t})}^{2} \geq 4 a$

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