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Slope of tang...

Question

Slope of tangent at a point of $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is $m$ and tangent passes through $(2 a, 0) . e$ is eccentricity of ellipse, then $3 m^{2} + e^{2}$ is equal to

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Solution

The correct option is B $1$
Equation of tangent is $y = m x \pm \sqrt{a^{2} m^{2} + b^{2}}$
Since, it passes through $(2 a, 0)$
Therefore, $0 = 2 m a \pm \sqrt{a^{2} m^{2} + a^{2} (1 - e^{2})}$
$\Rightarrow 3 m^{2} + e^{2} = 1$

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