The length of the latus rectum of the parabol | vedclass

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(A) The length of the latus rectum of a parabola is given by $L.R. = 2 	imes d$,where $d$ is the perpendicular distance from the focus $(x_1, y_1)$ t

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$2$

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(A) The length of the latus rectum of a parabola is given by $L.R. = 2 	imes d$,where $d$ is the perpendicular distance from the focus $(x_1, y_1)$ to the directrix $ax + by + c = 0$.The distance $d$ is calculated as $d = \left| \frac{ax_1 + by_1 + c}{\sqrt{a^2 + b^2}} ight|$.Given focus $(3, 3)$ and directrix $3x - 4y - 2 = 0$,we have:$d = \left| \frac{3(3) - 4(3) - 2}{\sqrt{3^2 + (-4)^2}} ight| = \left| \frac{9 - 12 - 2}{\sqrt{9 + 16}} ight| = \left| \frac{-5}{5} ight| = 1$.Therefore,the length of the latus rectum is $L.R. = 2 	imes 1 = 2$.

The length of the latus rectum of the parabola whose focus is $(3, 3)$ and directrix is $3x - 4y - 2 = 0$ is

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