The product of the slopes of the tangents to the ellipse $2 x^{2} + 3 y^{2} = 6$ drawn from the point (1, 2) is

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Solution

The correct option is C
$\frac{x^{2}}{3} + \frac{y^{2}}{2} = 1$
$y = m x \pm \sqrt{a^{2} m^{2} + b^{2}}$ is the equation of the tangent.
It passes through (1,2)
$2 = m \pm \sqrt{3 m^{2} + 2} \sqrt{3 m^{2} + 2} = m - 2 3 m^{2} + 2 = m^{2} - 4 m + 4 2 m^{2} - 4 m - 2 = 0 m^{2} - 2 m - 1 = 0$
Product of slopes = - 1

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