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The sum of the slopes of the tangent to the ellipse $x^{2} / 9 + y^{2} / 4 = 1$ drawn form the points (6, -2) is

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-8/9

3/4

- 6/7

answer is D.

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Detailed Solution

$\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1 \Rightarrow a^{2} = 9, b^{2} = 4, (x_{1}, y_{1}) = (6, - 2)$

Sum of the slopes of tangents $= \frac{2 x_{1} y_{1}}{x_{1}^{2} - a^{2}} = \frac{2 (6) (- 2)}{(6)^{2} - 9} = \frac{- 24}{27} = - \frac{8}{9}$

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