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Equation of Tangent in Slope Form

The equation ...

Question

The equation of tangent to the ellipse $2 x^{2} + 3 y^{2} = 6$ which make an angle $30^{\circ}$ with the major axis is

A

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B

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C

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D

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Solution

The correct option is A
Equations of tangents are $y = m x \pm \sqrt{a^{2} m^{2} + b^{2}}$
Here m = $tan 30^{\circ} = \frac{1}{\sqrt{3}}; a^{2} = 3; b^{2} = 2 \Rightarrow x - \sqrt{3} y \pm 3 = 0$

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