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How to derive the line of action of a conic from the slope of the line tangent to the conic?
The conic of an ellipse is defined as
$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.$
Suppose I know $a$ and $b$ and I want to find out the line of action of the ellipse. I.e., the line on which the ellipse will pass when rotated around its major axis.
The line of action is given by the set of points
$\left\{ \left(x \cos \theta, y \sin \theta \right) \ \middle| \ 0 \le \theta \le 2\pi \right\}.$
If I want to find the slope of the line of action, how can I go about it? I know that the slope is given by the angle
$\tan \theta = \frac{y}{x}$
and thus
$\tan \theta = \frac{b}{a} \ \frac{x 0b46394aab
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