If (0, 0) is the vertex and 3x - 4y + 2 = 0 i | vedclass

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(C) The distance from the vertex to the directrix is $a$. Given the vertex $(x_1, y_1) = (0, 0)$ and the directrix $Ax + By + C = 0$,the distance $a$

Vedclass · Accepted Answer

$8$

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(C) The distance from the vertex to the directrix is $a$. Given the vertex $(x_1, y_1) = (0, 0)$ and the directrix $Ax + By + C = 0$,the distance $a$ is given by: $a = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$ $a = \frac{|3(0) - 4(0) + 2|}{\sqrt{3^2 + (-4)^2}} = \frac{2}{\sqrt{9 + 16}} = \frac{2}{5}$ The length of the latus rectum is $4a$. Length $= 4 	imes \frac{2}{5} = \frac{8}{5}$.

If $(0, 0)$ is the vertex and $3x - 4y + 2 = 0$ is the directrix of a parabola,find the length of its latus rectum. (in $/5$)

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