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

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(D) The length of the latus rectum of a parabola is given by $2 	imes d$,where $d$ is the perpendicular distance from the focus to the directrix.The

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$\frac{14}{\sqrt{17}}$

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(D) The length of the latus rectum of a parabola is given by $2 	imes d$,where $d$ is the perpendicular distance from the focus to the directrix.The focus is $(x_1, y_1) = (2, 3)$ and the directrix is $Ax + By + C = 0$,where $x - 4y + 3 = 0$.The perpendicular distance $d$ is given by the formula:$d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$Substituting the values:$d = \frac{|1(2) - 4(3) + 3|}{\sqrt{1^2 + (-4)^2}} = \frac{|2 - 12 + 3|}{\sqrt{1 + 16}} = \frac{|-7|}{\sqrt{17}} = \frac{7}{\sqrt{17}}$The length of the latus rectum is $2d = 2 	imes \frac{7}{\sqrt{17}} = \frac{14}{\sqrt{17}}$.

$A$. $P$	$I$. $(2,0)$
$B$. $Q$	$II$. $(\frac{3}{2}, -\frac{1}{4})$
$C$. $S$	$III$. $(\frac{3}{2}, 0)$
$D$. $Z$	$IV$. $(\frac{3}{2}, -\frac{1}{2})$
	$V$. $(0, \frac{3}{2})$

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

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