Find the length of the latus rectum of the pa | vedclass

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Question

(A) The given equation is $y = x 	an \alpha - \frac{g x^2}{2 u^2 \cos^2 \alpha}$.Rearranging the terms to the standard form of a parabola $x^2 = -4ay

Vedclass · Accepted Answer

$\frac{2 u^2 \cos^2 \alpha}{g}$

Vedclass · Answer

(A) The given equation is $y = x 	an \alpha - \frac{g x^2}{2 u^2 \cos^2 \alpha}$.Rearranging the terms to the standard form of a parabola $x^2 = -4ay$:$\frac{g x^2}{2 u^2 \cos^2 \alpha} = x 	an \alpha - y$$x^2 = \frac{2 u^2 \cos^2 \alpha}{g} (x 	an \alpha - y)$.This is of the form $(x - h)^2 = -4a(y - k)$.Comparing the coefficient of $y$,we have $4a = \frac{2 u^2 \cos^2 \alpha}{g}$.The length of the latus rectum is $4a = \frac{2 u^2 \cos^2 \alpha}{g}$.

Find the length of the latus rectum of the parabola $y = x \tan \alpha - \frac{g x^2}{2 u^2 \cos^2 \alpha}$.

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