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Pair of Tangents from a Point

If α and β ar...

Question

If $α$ and $β$ are the eccentric angles of points of contract of tangents drawn from (3,2) to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ then $| t a n (\frac{α - β}{2}) | =$

1

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\frac{1}{2}

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5

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Solution

The correct option is A $1$
Point of intersection of the tangents at $α, β i n (a \frac{c o s \frac{α + β}{2}}{c o s \frac{α - β}{2}}, b \frac{s i n \frac{α + β}{2}}{c o s \frac{α - β}{2}})$
Which is given as (3, 2)
$\Rightarrow c o s^{2} (\frac{α - β}{2}) = \frac{1}{2}$
$\Rightarrow | t a n (\frac{α - β}{2}) | = 1$

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