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 defined as $4a$,where $a$ is the perpendicular distance from the focus to the directrix.
Given th

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$4$

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(A) The length of the latus rectum of a parabola is defined as $4a$,where $a$ is the perpendicular distance from the focus to the directrix.
Given the focus $S = (3,3)$ and the directrix $L: 3x - 4y - 2 = 0$.
The perpendicular distance $a$ from a point $(x_1, y_1)$ to the line $Ax + By + C = 0$ is given by the formula $a = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.
Substituting the given values into the formula:
$a = \frac{|3(3) - 4(3) - 2|}{\sqrt{3^2 + (-4)^2}}$
$a = \frac{|9 - 12 - 2|}{\sqrt{9 + 16}}$
$a = \frac{|-5|}{\sqrt{25}}$
$a = \frac{5}{5} = 1$.
The length of the latus rectum is $4a = 4 	imes 1 = 4$ units.

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

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