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If $\frac{x^{2}}{\sec^{2} θ} + \frac{y^{2}}{\tan^{2} θ} = 1$ represents an ellipse with eccentricity e and length of the major axis $l$ then

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$l^{2} - e^{2}$ is independent of $θ$

$e l$ is independent of $θ$

$l$ is independent of $θ$

$e$ is independent of $θ$

answer is C.

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Detailed Solution

$l = 2 \sec θ, e = \sqrt{\frac{\sec^{2} θ - \tan^{2} θ}{\sec^{2} θ}} = \cos θ$

$\Rightarrow e l = 2$ which is independent of $θ$

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