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If the eccentric angles of the extremities of a focal chord (other than the major axis) of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ are $α$ and $β$ then $\frac{\cot (α / 2)}{\tan (β / 2)} =$

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Detailed Solution

$\frac{x}{a} \cos (\frac{α - β}{2}) + \frac{y}{b} \sin (\frac{α + β}{2}) = \cos (\frac{α - β}{2})$

It is passes through (ae,0)

$\frac{a e}{a} \cos (\frac{α - β}{2}) + \frac{0}{2} \cos (\frac{α + β}{2}) = \cos (\frac{α - β}{2})$

$\frac{\cos (\frac{α + β}{2})}{\cos (\frac{α - β}{2})} = \frac{5}{4}$

Apply cofounded and dividend.

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